The classic Buddy Cop Show formula usually involves two law-enforcement officers with very different methods pairing up to fight crime. Older versions usually involve a By-the-Book Cop working with a Cowboy Cop. They will form an Odd Couple due to their views of regulation.
In recent years, new shows have partnered Cops and Scientists. Rather than squabbling over regulations, their Odd Couple differences come from their roles in each investigation, which brings out differences in personality. This may have something to do with the success of the CSI franchise, which highlighted the scientific side of law enforcement.
The Cop will deal with the elements of police work that involve dealing with other people such as interrogations, arrests, and dealing with superiors. If a fight breaks out, it will be the Cop who does the heavy lifting. The Cop will usually be Book Dumb but Street Smart.
The Scientist will usually be more of an ivory-tower intellectual with little practical experience in law enforcement. They will usually have personality quirks or No Social Skills (except when they're one-on-one with the cop). They might also be a Straw Vulcan. They will handle the CSI-style parts of the investigation and rarely do anything physical. If they interact with witnesses, suspects, or superiors, they'll either keep quiet or end up making things worse. Usually, Hilarity Ensues.
Despite their differences, both halves of the team come to respect each other and become an effective crime-fighting force. Bonus points if each demonstrates prowess in the partner's expertise at a key point.
It's important to remember that, to count as this trope, the Cop and the Scientist must have roughly equal focus. They must be partners. While many crime-themed shows have both cops and scientists, they might focus more on one or the other. If so, then that show does not count as this trope.
Compare Androids and Detectives.
- In I, Robot, Detective Spooner (Will Smith) is the gritty, cyborg cop and Dr. Susan Calvin (Bridget Moynahan) is the cold but beautiful robotics expert. They're investigating the death of another scientist, Dr. Lansing (James Cromwell).
- In Live Free or Die Hard, McClane (Bruce Willis) is an experienced police officer with a checkered past, and Farrell (Justin Long) is a "grey hat" hacker on the run from both police and organized crime. They join forces against a tech-savvy terrorist who's trying to kill them first.
- Wild Wild West features Jim West (played by Will Smith) as the Cop while Artemis Gordon is the Scientist.
- Barrett Coldyron of R.O.T.O.R.combines both roles in one character.
- Earlier books in The Dresden Files have a Cop and Wizard dynamic, with Karen Murphy (the cop) hiring Harry (the wizard) as a consultant when she has to work a case involving magic.
- The Temperance Brennan novels by Kathy Reichs, which Bones is based on, have Dr.Brennan the scientist and her on again off again boyfriend Detective Andrew Ryan.
- Rizzoli & Isles, respectively.
- Don and Charlie, the mathematician, from NUMB3RS.
- Rosemary And Thyme, two "gardening detectives." One is a former police officer and the other is a professor.
- In The Sentinel, a cop with Super Senses works with an anthropologist who helps him understand his abilities.
- Both the UK and American versions of Eleventh Hour feature a scientist teamed with a law enforcement officer/bodyguard (from Special Branch in the UK and the FBI in the US).
- Also seen on Body of Proof, where the scientist (Dana Delany) has both her usual medical investigator (the blonde guy) and some actual cops whose cases she usually ends up working on (the fat guy and the black woman).
- Eureka has Sheriff Jack Carter and the entire town of Eureka, which is populated by Mad Scientists. The typical episode involves one of the town's scientists accidentally causing a strange problem and Jack working with the scientists to solve it. Henry, who is also the coroner/forensics expert is usually the scientist to Carter's cop.
- Everyone in NCIS is very fond of their Cloud Cuckoolander lab techs, Perky Goth Abby Sciuto and Absent-Minded Professor Donald "Ducky" Mallard, who, rarely for a cop show, are markedly less combat-ready than their field agent co-workers. But still no slouches.
- NBC's Hannibal, based on Red Dragon, in which Will Graham partners with psychiatrist Hannibal Lecter, not knowing that Lecter is himself a serial killer.
- Luther involves a police officer named Luther working with Alice Morgan, a scientist and murderer who hid her crime so skillfully that not even Luther can prove her guilt.
- Bones has Booth and Brennan, the cop and scientist respectively.
- Criminal Minds: Unusual example, Reid is one of the FBI agents, but his extensive knowledge allows him to also act as the scientist when they need it.
- Fringe has the lovely Agent Dunham and Cloud Cuckoolander in residence Dr. Walter Bishop.
- For a loose interpretation of the trope, Castle is a novelist partnered with Detective Beckett (This arrangement is so he can get inspiration for his books. He was able to make it happen because he's friends with the Mayor.) In a variation, both have considerable people skills, but in different areas.
- While The Flash (2014) isn't really about this trope, sometimes investigations fall into the same pattern due to main characters Barry Allen (CSI) and Det. West. Until Barry becomes The Flash, that is.
- Forever stars Dr. Henry Morgan, a medical examiner, and his partner, Jo Martinez, a streetwise detective. Shows the evolution of the trope, as the Cop and Scientist back and forth serves as more of a backdrop to the more central focus on Dr. Morgan's immortality.
- Galileo, with police detectives Kaoru and Misa (in their respective seasons) and physicist Manabu Yukawa, the titular Galileo.
- the CSI series all have elements of this. Jim Brass in the original CSI borderlines this. The other members of the franchise focus more on the science, and CSI: Miami's resident non-scientist is more supervisory, but in CSI: NY, Flack works alongside the scientist detectives under Mac, making the policework and science more equal and making it closer to this trope.
- Repeatedly parodied in Dr. Boli's Celebrated Magazine with such fictional TV shows as "Harsh Words", where a by-the-book cop is partnered by a cold yet beautiful Forensic Etymologist.
- Paradigm Shift mixes this one with the traditional Buddy Cop routine. Mike and Kate are the standard By-the-Book Cop and Cowboy Cop respectively, albeit downplayed significantly in Mike's case, but Gina the medical examiner is By The Book to the point of unreasonable at times. She also has the limited people skills part down pretty well, not that Kate doesn't also have her moments.