So you're watching your favorite high school drama. In comes the cheerleader, as bubbly, bright and ditzy as ever. Everything about her, from her Valley Girl vernacular to her superficial interests and appearance, tells you that this is the classic mold of The Ditz.
That is until the episode goes on.
This young woman is revealed to be a straight-A honors student. She is a master when it comes to hacking computers, or has a wealth of talent in dealing with mechanical things. Her knowledge of things both vast and obscure makes the viewer do a double take in their perception of her. There's a sort of cognitive dissonance that goes on, juxtaposing the character's appearance against their actual intellectual ability. This character makes you say "Huh... you're Smarter Than You Look".
This character is not simply the Genius Ditz or Rain Man, for those characters are sharply skilled in a single area while remarkably hindered in others. The Smarter Than You Look character has true vast and all-encompassing intelligence. He just looks stupid, through mannerisms, vernacular or visible appearance, while actually being quite smart. The key to being Smarter Than You Look is the distinct and clear appearance of stupidity.
This is not to be confused with Obfuscating Stupidity, where a character consciously plays dumb either to avoid responsibility or for some other reason. This trope has no intention of appearing to be unintelligent; they simply can't help the appearance of stupidity they have.
The Bunny-Ears Lawyer can overlap with this, but the difference is in the appearance of the character. The Bunny Ears Lawyer appears strange, but it doesn't take away from his intelligence. He is typically known to be a genius. The Smarter Than You Look appears stupid, and this appearance conflicts with their actual intelligence. A genius professor who always wears a wizard's hat to class and only answers to "Merlin" is a Bunny Ears Lawyer; one who can't read and has poor pronunciation skills would be a Smarter Than You Look.
Sometimes, the appearance of stupidity or ditziness is compounded by the presence of Unfortunate Implications, particularly racial or related stereotypes (This can be particularly true for those who are Pretty Smart for a Hottie, where beauty can belie a character's knowledge).
To an extent, this trope is subjective based on what the viewer (or the rest of the cast) view as unintelligent. In many cases, though, the character is consciously designed to have this appearance, to teach the audience An Aesop of never judging a book by its cover. Sometimes as tropes evolve the subversion can actually become the rule; for instance many modern viewers have grown to expect a character like the Valley Girl mentioned at the start to fall under this (because the 'surprise' has been used so often) and are thus themselves surprised when the character turns out to be genuinely ditzy.
The Smart Guy in a Five-Man Band may start out as this, or he may stay as this. The Absent-Minded Professor is often a subtrope of this. If the character is assumed to be stupid because he looks like Dumb Muscle, he's a Genius Bruiser. (This may be compounded by the character having a case of Face of a Thug.) This trope is to intellect as the Old Master is to strength, or as the Killer Rabbit is to danger/terror. This trope is a very close relative of Ditzy Genius, but differs in that the Ditzy Genius actually is pretty stupid/inept/Cloudcuckoolanderish sometimes, whereas the Smarter Than You Look character just has a ditzy personality.
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Anime and Manga
Gaoh of Eye Shield 21 who comes very close to being the monster version of this trope. Only the quarterbacks, Hiruma and Kid, notice that he might be a 7 foot raving dinosaur that can lift a car with ease, but he'll never, ever break the rules of football. His strategy is to break the enemy quarterback's arm, and if the quarterback doesn't have the ball, they'd get a severe penalty. Thus, he'll come to a screeching halt, even if he's tongue distance away from the quarterback, if they manage to throw the ball away at the last second.
Fullmetal Alchemist: 2nd Lt. Heymans Breda looks like a big dumb grunt, but he's actually pretty bright. Our first glimpse of him comes as he's gloating about winning atshogi for the 47th time in a row. The end of the flashback chapters about the war note why Mustang took on the subordinates he did. Breda's in the group because he's smarter than he looks.
Shiro Kabuto from Mazinger Z and its sequel Great Mazinger. He did not come across like very smart, and in fact during his first few appearances, his acts make him looking like Too Dumb to Live (for starters, while Koji is horrified by the Iron Mask, especially after killing it, all Shiro says is that Koji is so cool for killing him). Later on in the series, he shows being more mature than his older brother, proves he is knowledgeable about things the teenagers around him are completely ignorant of, learned to pilot the Pilder in relatively short time (bonus points since unlike Koji, he has practically zero experience in piloting the Pilder, while Koji mentions that the control is similar to his motorbike) and pulls a Big Damn Heroes several times, that really says something. Of course, he IS a member of the Kabuto family: his grandfather and his father were excellent scientists, and even his Idiot Hero brother can be very clever when he uses his brains, so you can tell it is on the blood.
Ino Yamanaka of Naruto appears to be the outgoing, bubbly rival and has tendencies of a Dumb Blonde. However, in the first Naruto databook, it is revealed that Ino had the best overall grades in the Academy.
Deidara has all the subtility and grace of a Mad Bomber and appears not very bright. His tactical skills are nothing to scoff at and the Naruto databook rates him a 4.5/5 for intelligence, making him smarter then geniuses like Sasuke and Neji.
Kanon in Servant × Service. Despite her being the show's Token Mini-Moe, her cute looks belie a smart, perceptive mind. She can fix her father's stuffed bunny avatar rather easily, having spent her childhood watching her mother do it, and also instantly deduced from Touko's statements that her brother and Chihaya are dating.
Bunnie Rabbot from the Sonic the Hedgehog comics can be an example of this. With her thick country accent and naïve optimistic attitude, you'd never expect her to be so technologically skilled and resourceful. Granted, she's never really shown to have vastly diverse intellect, so she may fall somewhere between this trope and the Genius Ditz.
Legion of Super-Heroes: Dream Girl in the modern/original version. Like many story elements in the Legion, this was based on a throwaway reference from the Silver Age: she changed Light Lass's powers using Naltorian Science. She's the smartest Legionnaire after Brainiac 5, Superman, and Supergirl, at least if you believe the RPG, and is one of the few who has been able to use Brainiac 5's force shield belt.
In Hogwarts is a Strange Place Hermione initially dismissed Harry as unintelligent because of the rural speech pattern and dress due to having spent most of his childhood on a farm in Iowa, yet he loved books and was well-read enough to quote poetry to her. His explanation of it was "There's just too damn much work ta be done on a farm to waste time in front of a TV. Most folks I know would rather read a book than let some piece of gadgetry do their thinkin' for them."
Legally Blonde: The main character, Elle Woods, becomes this. While maintaining many of her ditzy qualities (printing a résumé on scented paper, for instance), she becomes a highly self-sufficient, skilled lawyer, and shows remarkable intelligence overall (particularly in the sequel).
Me, Myself & Irene: The triplets are a great example. They have all the vernacular and visible qualities of gangster-wannabes, but are all complete geniuses. This is one that is compounded by some racial Unfortunate Implications.
Guido looks like dumb muscle. He has a degree in business, even if he had to take Economics 101 three times. He just prefers hands-on kneecapping to the cruelty of slowly sucking out someone's life in a business environment.
Nunzio is Guido's bookend-matching cousin. He's taught kindergarten, requiring a four-year degree in many dimensions, and was an animal trainer at one point. Gleep considers him slightly more intelligent then most of Skeeve's friends. This opinion occurred after Nunzio got Gleep -a baby dragon- to 'sit' by stopping him cold in full run with his hand on his nose.
Chumley hails from Trollia, is huge with different-sized eyes, and can troll-speak with the best of them. He's also a vegetarian and speaks in a refined manner and accent in private. He can discuss learnedly on many of the subjects that come up through the books, and tell what damage his sister is doing in a bar fight just by the resultant sounds.
Rachel from Animorphs may count. She's a major shopping enthusiast, blonde, beautiful... and a straight A student who also happens to be a Blood Knight. The Ditz and Blood Knight aspects of her personality are even split at one point.
Glee: Quinn might be expected to be the dumb, beautiful, bitchy head cheerleader, but it turns out she only fulfills three-quarters of this. She seems pretty intelligent for most of the series (except, y'know, the whole teen pregnancy thing) and is mentioned at one point as a straight-A student. Her boyfriend, stereotypical non-Jerk Jock Finn, is correspondingly dumb. Early on in season 3, which is considered to be the height of her stupidity decision making-wise, it is revealed that she was on honour roll with a straight 4.0 GPA during her teen pregnancy, and that she's been accepted early into Yale, despite the fact that she by this point had a history of playing truant. She's also been known to use a varied and polysyllabic vocabulary, and she has given some insightful, wise, eloquent advice to Rachel/Santana/Mercedes.
Intelligence has a really good perception example. Gabriel doesn't want a handler, so he's basically harassing Riley Neal through her digital footprint to get her to go away. He mentions her low SAT scores and she says defensively, she doesn't do well on tests and he sort of brushes off that answer. In that same episode, she corrects his digital interface Mandarin and proves (through simple logic and deduction) to his boss, Lillian Strand, that A) Strand does actually believe the same things as Gabriel. His wife was an undercover agent, who seems to have turned on her country and died. Gabriel believes she's alive and loyal. And B) actually sort of talks Strand into taking action to help Gabriel when she was previously telling him to forget about the issue. Two things, Gabriel hadn't managed to do himself even though he had all of the facts of the situation and Riley didn't.
Jayne Cobb from Firefly. He can read people much better than books and even gets a reluctant praise from his interrogatee in those very words.
Eliot on Leverage as The Big Guy is often not seen as useful for his inteligence. However he is also a Chef of Iron and learns quite a lot from his various girlfriends. It is even a Mad Libs Catch Phrase: I've dated a lot of [Insert useful profession]. He's also occasionally taken over for Nate. His intelligence was even lampshaded by Nate, when Maggie mentions that he's smarter than he seems in The Zanzibar Marketplace Job and Nate says that it's kind of the point. It comes all the way back around with Sterling.
Sterling: Your friends' lives hang in the balance and you're going to take your cues off a punch-up artist instead of me?
In Series Five of the new Doctor Who, Rory Williams initially looks like the dim, dreary sort-of boyfriend Amy will happily ditch to go travelling with the Doctor. Then you realise that while the whole of Leadworth is outside taking photos of the Sun apparently going out, Rory - the nurse - is paying attention to the coma patient out walking his dog, and taking photos of that. That's right, Mickey Smith 2.0 just identified Prisoner Zero all on his own with no help from the Doctor, and did the one thing that would let the Doctor give the Atraxi all the information they needed to catch it. There's a reason the Doctor beams at Rory like he's just got a new crush at the end of their first conversation.
Rory's first time venturing into the TARDIS also has him completely non-fazed with it being Bigger on the Inside, explaining that he's read up on all the latest scientific theories since they last met.
Lister from Red Dwarf often demonstrates that he's actually a great deal smarter than Rimmer, but their personalities and dress sense would indicate otherwise. The only reason Lister is a lower rank than Rimmer is because he's perfectly happy being a Brilliant, but Lazy slob.
One episode of Malcolm in the Middle had Malcolm get paired with a ditzy popular girl during chemistry class, and is quite surprised when the "ditz" part of her persona is an act. Turns out, she's nearly as smart as Malcolm himself, but to her, being popular is more important than being smart.
Howard Stern: Despite having plenty of toilet humor and naked women on his show, Stern is a graduate from Boston University and is well-versed in current events.
Final Fantasy X has Rikku. Despite having a somewhat naive bubbliness, being a bit clumsy, and overall having many mannerisms of The Ditz, she is a crack mechanic, skilled chemist, master thief, talented with computers and machinery, and shows significant emotional and intellectual depth.
Ox in Visions & Voices. He's a generic farmer who talks in a country accent and is the party's Mighty Glacier, yet if you talk to him you'll find that he's actually very intelligent and loves books. Perceptive players will notice right off the bat that his secondary stat is even the game's spellcasting stat, to further reinforce this.
This is even hinted at in his "Meet The..." trailer: his "400,000 dollars to fire this weapon for twelve seconds" line speaks of some serious math skills.
The Scout is a loud-mouthed egotistical punk, but some of his dialogue hints at some brains behind the bragging: taunts towards the Medic and Demoman reference the Hippocratic Oath and depth perception, respectively, and the Halloween update also had him reference Lovecraftian literature while trash-talking Merasmus.
Mass Effect 2 has Grunt from the same species who, despite essentially being a newborn test-tube baby, is very articulate. And when he's not killing big things, he enjoys listening Ernest Hemingway. His favories seem to be 'For Whom The Bell Tolls' (which is a notoriously graphic rendition of the Spanish Civil War) and 'The Old Man and the Sea' (which is an old fisherman fighting off sharks). He's got barely a tenth into 'The Sun Also Rises,' and outright deleted 'A Farewell to Arms.'
Prototype 2 features James Heller, a Marine who can rip the turrets off tanks and finds every opportunity to slip in a curse in every sentence. However, he definitely has a sense of humor (if a little dark), has a keen knowledge of tactics, and the collective knowledge of several doctors all contained within his mind.
Tojiko in Kara no Shoujo looks pretty dumb and is rather easy to tease, but she actually gets good grades and is a publishing author.
Makoto Nanaya of BlazBlue gives the appearance of a bubbly and scatterbrained squirrel beastkin with more exposed skin than working intellect... until a flashback in Noel's story mode reveals that she, a mere commoner among individuals of more prestigious families, was attending the NOL Military Academy entirely on scholarship. Were that the extent, she wouldn't qualify, but an ivory tower environment like a classroom is a poor place for her to apply her immense street smarts, yet work in the Intelligence Division under Captain Hazama and as a Double Agent slash Reverse Mole for Sector Seven is. Continuum Shift in general, especially Slight Hope (Makoto's Story mode), is a demonstration of her prowess as an Intelligence officer - put short, had Makoto known that she had fallen into a timeline where Noel never existed and her activities in Slight Hope were interfering with his plans, Hazama would be treating her as something much worse than a mere Spanner in the Works. That intro discussion at the top of the page? That's Hazama expressing his purest scorn for Makoto for almost obliterating his plans again.
Flonne, in Disgaea: Hour of Darkness is a ditzyLove FreakOtaku angel, but she's shown to be more with it than you'd suspect. (Laharl even says so at one point). Similarly, Laharl is a bratty, selfish, and violent demon, but has been prone to making cool-headed judgement. When he issues out a challenge for the title of Overlord, the Prinny commentary on the DS version shows surprise at Laharl's skill at calligraphy...because it didn't know Laharl could spell.
Done in an odd way in Sluggy Freelance, maybe subverted, with Clem. Zoë meets up with him for the first time in years, after he supposedly dropped out of high school. He's dressed like a janitor, has a "dumb" accent and walks around holding roadkill in his hand. Yet, it turns out he didn't drop out of high school so much as advance much faster than everyone else and is now a professor at the local university, and the roadkill (reportedly) is for stem cell research. The possible subversion is that he's still a moron with a dumb accent who walks around holding roadkill. His intelligence is intentionally left on the level of Informed Ability.
The main character of Blade Bunny acts very much like a stereotypical Dumb Blond ditz. But she's a highly skilled ninja who, on a second or third read, is clearly thinking ahead about five steps from her opponent.
Likewise, Tsukiko. Don't let the Girlish Pigtails or the crush on Xykon fool you — during her fight with Haley she came up with some pretty good ways around her evasions, and she figured out something Xykon himself had been unaware of: that the ritual for the Snarl doesn't do what Redcloak had been telling them it did.
Vanamonde von Mekkhan. His grandfather kind of names the trope. Most of the time, he is comparing flavors at the coffee shop (it's unclear whether he has an actual job there). But when the city is attacked, oh my. 
Agatha admits that Tweedle is smarter than he looks, but that she is too. When Violetta says that Agatha looks pretty smart already, she immediately realizes that that was what Agatha was actually going for.
Zola. She's blonde and pink, giving a great Valley Girl impression, and in front of Gil is constantly a distressed damsel. But she packed a small personal arsenal into Der Kastle, killed at least one person in cold blood as a warning, and showed herself to be a cunning, ruthless, and strong fighter. She also outwitted Lucrezia!Other!
While Leviathan from Worm is already a Hero Killer by virtue of consistently slaughtering a full fourth of the army of superheroes and villains that show up to fight him every time he appears to destroy entire cities, and is strong, faster than a superspeedster, and has large-scale hydrokinesis that completely averts Soft Water, the Extermination arc also reveals that he possesses a kind of brute cunning, inventing new tactics to defeat Armsmaster's prediction software on the fly.
Stewie from Family Guy: Simply because he's a baby, he's assumed to be unintelligent, until you find out about his plans for world domination, mastery of multiverse theory and so forth.
Vivian Porter in the Kim Possible episode with the robot rumble. She's blond, tanned, gorgeous, apparently ditzy, and even voiced by Shawnee Smith, a well-known ditz player... except she makes her own robots. Including an artificial "boyfriend" created specifically to provide an alter ego because she thinks her looks will prevent people from taking her seriously.
In The Simpsons story about the Hellfish group, the big guy, named "Ox", has a stereotypical stupid guy voice and is the one who explains the concept of tontine to the others.
Burns: "Well put, Oxford."
Burns does it to Homer in another episode:
Burns: "You're smarter than you look. Or sound. Or our best tests suggest."
Barney Gumble may be a drunkard and lazy, but he has shown to process exceptional talent when it comes to the arts.
In Homer's Barbershop Quartet, Barney is a brilliant singer.
In Mom and Pop Art, Barney drew a replica of the famous painting, Sunday Afternoon on the Island of La Grande Jatte by Georges Seurat, on a napkin.
Mission Hill: Jim, Andy's best friend doesn't seem all that smart. A slow talking, monosyllabic guy, who is implied on more than one occasion to be a stoner. But apparently, he's also a total computer whiz, and paid very well for it by an ad agency. Andy wasn't even aware until Jim told him.