Ambition Is Evil: Kayle, Oda's brother: he wanted power, and managed to get the attention of the Midnight Mayor. To the point he sent Aldermen after him, out of London. Bakker, who tried to enslave the blue electric angels to achieve immortality, is a somewhat more subtle example.
Animorphism: Charlie. In true Swiftverse fashion, he can turn into several urban animals, including a pigeon and a fox.
The Death of Cities from The Midnight Mayor is a relatively straightforward example. Naturally, the Aldermen are hesitant to believe his claim is real.
Matthew himself is a slightly more complex example; as of the end of the second book he arguably personifies both the city of London and telephony.
The gods of this world are personifications of urban life and archetypes, including but not limited to The Bag Ladynote an apparently crazy old lady who wheels a cart full of shopping bags filled with animals that attack on her command, The Beggar King, and Fat Ratnote a literal giant rat with wire fur who roams the subway.
Lady Neon is implied to have some characteristics of this as well, specifically unattainable, unrealistic glamour.
In A Madness of Angels, "Make me a shadow on the wall" and "Give me life!"
"Waiting for you at the end of the alley" in the Neon Court.
"You can't save everyone" in The Minority Council
Art Attacker: The White Clan. They use graffiti for all their magic, including creating painted attack animals that come off the walls and fight for them.
Art Initiates Life: During the battle against Lee, the paintings on the walls came to life and fight. We also learn in The Midnight Mayor that Vera is actually made of paint.
Awesome McCoolname: The bikers tend to change their names: Dave to Blackjack; Laslie to Halfburn. Also, Jeremy the Troll wants to be called the Mighty Raaaarrggh!. He lightly mocks Matthew for having a normal name.
Back from the Dead: Matthew Swift, who quickly tires of explaining why he isn't dead and eventually just answers "I got better."
Backstory: How Matthew met Bakker, how Matthew met Dana, how Oda became part of the Order, how Blackout was defeated...
Badass Adorable: Matthew: channeling beings of pure energy, and forging alliances eating pancakes and ice-cream.
Badass Biker: The Bikers, who besides being standard bikers with all the implied badass can slip through space to travel huge distances in a blink.
"I was the apprentice of Robert James Bakker. I'm sure you've heard of him. I am a sorcerer. I was there when Bakker died. We... made it happen. I too have met death, and did not have to peel the bones away from my chest to survive the encounter. I am also, and incidentally, the Midnight Mayor, the blue electric angels, the fire in the wire, the song in the telephones, and we are having a bad week. Be smart; fear us." ... "We are the blue electric angels! We were born from the leftover breaths of humanity, by the fears and the thoughts and the ideas and the truths and the lies you poured into the telephone lines. We were created by you bigger and brighter and more alive than any mortal could aspire to be! Do not think to tell us what we can or cannot do! Where is her hat?!"
In The Neon Court too:
"We are the Midnight Mayor, protector of this city, carrier of its secrets and bearer of its shadows. The shadows watch us as we pass, the pigeons turn away at our passage, the rats scurry beneath our feet and shudder at the sound of our footsteps on the stones. We are the blue electric angels, the telephones sing at the passage of our voice, our blood is blue fire, our soul carries a pair of angel wings. We are the killer of Robert Bakker, sorcerer, master of the Tower; we destroyed the death of cities; we came back from the dead, Swift and the angels, two minds became one, two souls in one flash, in one form, in one voice. We are me and I am we. And we're frustrated."
And The Minority Council:
"My name is Matthew Swift. I'm a sorcerer, the only one in the city who survived Robert Bakker's purge. I was killed by my teacher's shadow and my body dissolved into telephone static and all they had left to bury was a bit of blood. Then we came back, and I am we and we are me, and we are the blue electric angels, creatures of the phones and the wires, the gods made from surplus life you miserable excuse for mortals pour into all things electric. I am the Midnight Mayor, the protector of the city, the guardian of the night, the keeper of the gates, the watcher on the walls. We turned back the death of cities, we were there when Lady Neon died, we drove the creature called Blackout into the shadows at the end of the alleys, we are light, we are life, we are fire and, would you believe it, the word that best describes our condition right now is cranky. Would you like to see what happens when you make us mad?"
Badass Grandpa: Robert Bakker, to the point he's still a very powerful (and dangerous) sorcerer even after a stroke.
Badass Longcoat: Matthew wears one, enchanted to make him totally unnoticeable. He gets it in relatively pristine condition in A Madness of Angels; by the end of the series, it's stained and has been mended with red thread, but he still wears it. And of course, it is still just as badass.
Badass Normal: Oda, who despite having no magic of her own in any form managed to outlive some of the most powerful people in the series.
Barbarian Tribe: The Tribe. They mutilate themselves to increase their power.
Big Damn Heroes: The Bag Lady and later Oda in A Madness of Angels; Penny in The Neon Court.
Black and Grey Morality: With the number of bodies he leaves in his wake and his utter ruthlessness when he dedicates himself to a cause, Matthew would probably the bad guy if his enemies hadn't already well and truly crossed the Moral Event Horizon.
Blood Magic: In the first book, Matthew uses his blood to keep Sinclair alive and convinces everyone to sign a blood oath which kills The Mole when he betrays them. And it's an oft-repeated point that the blood of the blue electric angels would go for huge prices on the black market, presumably to cast all kinds of magic.
Bullying a Dragon: Played straight with Chaigneau, who had the brilliant idea of kidnapping Matthew, beating the crap out of him and blackmailing him (yes, the guy who happens to be a sorcerer and to channel beings of pure energy. It's not like he can curse him). Averted with Matthew: people consider his plans to destroy the Tower Bullying a Dragon, while Matthew knows he can do it.
Came Back Strong: Matthew. Not that Matthew Swift the brown-eyed sorcerer was a weakling, but Matthew Swift the blue-eyed-sorcerer-cum-blue-electric-angels is something else again.
Came Back Wrong: Oda in The Neon Court. Many people think this happened to Matthew as well, although he (and the angels) disagree.
Cloud Cuckoo Lander: The Angels in the first book are drunk on life. When Matthew decides to take a day off from slowly but surely destroying the Tower, he lets the Angels go to a movie theater, play on a kids' playground, and eat ice cream, all to their amazement and extreme pleasure. The (very) few times Matthew and them do (very subtly) disagree on something, it's usually a throwaway line along the lines of "We wanted to -insert doing something not particularly appropriate to the situation at hand- but I didn't think it was the time."
Disappeared Dad: Matthew talks about his mother and grandmother, but never says a word about his father.
Disproportionate Retribution: What happens to Mo and the other kids in The Midnight Mayor. Generally speaking, stealing someone's hat doesn't warrant dissolving into ink or being torn apart by ten thousand paper cuts.
Doctor's Orders: Dr. Seah cheerfully accepts that Matthew probably isn't going to stop showing up broken, bruised, and bleeding on her doorstep, so to make up for it she gives him stern orders to take it easy (which she knows he won't do) and pain meds. Lots of pain meds.
Fantastic Drug: Fairy dust in Minority Council is a super-addictive drug that enhances the magical talent of the user ten fold. It's also made out of the ashes of previous users, as prolonged use turns you into dust.
Fire-Forged Friends: Matthew and Oda zig-zagged it most of the time (mostly because Oda kills sorcerers to make the world a better place) but their friendship is confirmed in The Neon Court, in the most traumatic and heart-breaking way ever.
Freaky Is Cool: Penny's reaction to Nabeela's technological medusa hair.
Penny: That is so totally fucking awesome. I'd, like, kiss her if my heart wasn't already given to a guy called Femi.
Matthew: You'd kiss Nabeela?
Penny: Jesus, wouldn't you?
Gods Need Prayer Badly: Since the current set of urban "gods" are there because people believe in them and pray to them, presumably there were others before. The Neon Court also exists because the old Fair Folk weren't getting the power they needed once life moved to the cities.
Go Out with a Smile: Vera, who while dissolving into paint smiles and smashes an Alderman over the head with a teakettle.
Gorgeous Gorgon: Nabeela in Minority Council. While her grandmother had traditional snakes, she was born with living wires and cameras instead.
Golem: The Litterbug sent after Matthew in the first book is a golem made of garbage and refuse.
Incredibly Lame Pun: A golem made of spilled trash, against whom a garbage can lid is a shield, is called a litterbug.
Intoxication Ensues: In Minority Council, while the angels are super charged from the fairy dust and destroying everything in sight, Matthew's narration is him giggling in the back of his head, going off on tangents about furniture and unaware as to what is actually going on.
The Angels: This is glorious! this is freedom, this is a drug of lava, a pit without end, liquid heaven, this is majestic!
Matthew So, yes, I think I might be a little stoned. I mean, not in a bad way, just you know... a little bit...
Chaigneau: You... blue electric angels... you are children with the power to kill, destroy and burn. You know nothing about life, its rules, norms, laws and understanding, and probably care less. Why should you not set the field on fire for the prettiness of its burning; why should you not kill wherever you go, simply because you can; why should you understand anything that the rest of humanity can?
Necromancer: A few pop up. Their MO is that they tend to try their hand at immortality by swallowing papers with the traits they wish they had in a golem-esque way. They die as soon as the paper is taken out, but in the meantime, they "live" exactly to the constraints of the paper (meaning if you forget to, say, write down that you still want to see colors or actually feel things, your life undead won't be very pleasant).
Never Found the Body: After Matthew died, his body disappeared; he was only known to be dead because his coat was found in a giant puddle of his blood. It turned out that his body had been absorbed along with his soul by the blue electric angels, making his/their later resurrection possible.
Omniscient Council of Vagueness: The "concerned citizens" from A Madness of Angels know a frankly frightening amount about Bakker's lieutenants, right down to judging San Khay's taste in men, and their name could hardly be vaguer.
Our Angels Are Different: The blue electric angels aren't "angels" in any sense we would recognize; rather, they're the product of the life that's been spilled into the phones over the years.
Powered by a Forsaken Child: Quite a few of the more clandestine services offered by the Tower are like this, including San Khay's offered "experience of a dying addict's final high." The Fairy Dust from The Minority Council also qualifies, especially Templeman's version.
Power Source: Cities, for urban magicians: take one of them to the country and his powers will be severely weakened, or nullified. There are stated to still be rural sorcerers, who are presumably just as useless in a city.
Power Tattoo: San Khay's magical tattoos, which afford him considerable stamina. Unfortunately, disrupting the patterns by dousing him with more ink ruins that power.
Pre-Asskicking One-Liner: Averted in The Midnight Mayor, as Matthew delivered one and run away. Given the situation, however, managing to escape alive was a victory.
Reasonable Authority Figure: Nair, the previous Midnight Mayor, was apparently one of these to the point where, even after his death, the Aldermen ultimately decide not to kill Matthew out of sheer respect for Nair's decision.
Straight Edge Evil: San Khay, who lives a fiercely regimented lifestyle, exercises hard, always eats healthily, and never partakes in smoking or drugs. However, his well-planned routine does permit him a one-night-stand twice a week...
Switching P.O.V.: A slightly odd example. Everything seemingly takes place from Matthew's perspective; however, the narrative switches back and forth between "I" and "we" to signal the distinction between the thoughts of Matthew and the blue electric angels who are possessing him. (Though they rarely if ever seem to disagree on anything.)
Tranquil Fury: Matthew frequently explains how angry he is in a totally flat voice. Of course, this is frequently due to utter exhaustion rather than actual tranquility.
Unequal Rites: Though wizards (who control magic through rules) and sorcerers (who draw on raw magical power) get along reasonably well, they both have very little respect for warlocks, who earn magical powers by bargaining with the various spirits in the area.
Well-Intentioned Extremist: Templeman. In the end, he wanted the Alderman to evolve and Matthew to understand what it means to be Midnight Mayor
Templeman: What does it take? What does it take to make you do it? How many more must I kill, how much worse things must become, before you do what has to be done? What is the point of you?!
What the Hell, Hero?: In A Madness of Angels Matthew gets a few of this about the casualties his revenge is going to cause.
Whodunnit to Me: The plot of the first book has aspects of this, though Matthew figures out the "who" pretty quickly and moves on to "how", "why", and "what can I do to get revenge".
Willing Channeler: Both Matthew and the angels are perfectly content to share a body, though the original combination was largely accidental.
Wound That Will Not Heal: Matthew suffers minor injuries by Hunger, and the wounds keep bleeding until he goes to the magical hospital.
X Marks the Hero: The Midnight Mayor always has two crosses carved in the palm of his hand.
X Meets Y: In universe, Matthew is described with these words: "The Swift-angel creature, while appearing almost entirely human, is at its core a combination of a traumatised dead sorcerer and infantile fire.". Then there's Matthew's definition of dragon: "Dinosaur meets flamethrower with wings".
You Do Not Have to Say Anything: In The Minority Council, used in an incantation to catch a monster (along with a roll of police tape and similar paraphernalia).