Almost every Marvel hero, even the ones that don't immediately come to mind as fighters, have an incredibly distinct combat style based around their unique abilities. For example, Black Widow and Captain America are two of the best martial artists in the MCU. These two characters alone showcase an incredible amount of training from a wide array of disciplines.
MCU fighting styles showcased throughout the various MCU hand-to-hand combat scenes are all developed with the help of incredible real-life martial arts masters. These trainers work together with the filmmakers to develop a unique style for each character based on their powers and background. This way, not only do the characters have their own styles that work with their powers, but they also have styles originating from real-world disciplines.
When Nick Fury visited Steve Rogers in TheAvengers, Rogers was finding peace through boxing. The gym Rogers was set up in had a noticeably 1940s aesthetic. The man out of time was clearly at home practicing a semiforgotten American sport in a gym that reminded him of his actual place in the timeline.
In Captain America: The First Avenger, Rogers fought like a 1940s strongman. As Chris Evans put it, in the first film, Rogers's style was more about throwing haymakers than getting technical. Evans went on to say that with the sequel, "His fight style needs to advance a little bit... There needs to be a style of fight. There needs to be a consistent display of strength."
In contrast, the opening scene of Captain America: Winter Soldier displayed a Rogers who was now flipping, kicking, and displaying all sorts of fighting styles. Rogers's advanced fighting style was to show he was constantly learning and bettering himself in modern times, as the filmmakers felt "bringing Steve Rogers into the modern-day also meant that he had studied and mastered modern fighting styles and techniques."
Black Panther was an incredible fighter across his various MCU appearances. It makes complete sense he's an expert fighter, considering T'Challa was trained since birth to one day become the warrior king of his nation.
T'Challa's training was best displayed in his de-powered fight against Killmonger. In that fight, T'Challa showcased his knowledge of capoeira, which is an acrobatic martial art that originated in Africa. In that same scene, T'Challa's weapons of choice showed he was proficient in Ukungcweka, which is known for using three weapons simultaneously. Specifically, a shield and blocking stick in one hand and an induku in the other hand.
Chadwick Boseman's trainer, Marrese Crump, stated he taught Boseman capoeira, but also Filipino martial arts, muay thai, and many others. According to Crump, "There are a lot of action movies that relegate to one certain style, and all of the fights look the same. Because of who T’Challa is, who the character is - a master of many - we couldn’t do that. We wanted to create a freedom in the fights that showcased how adaptable T’Challa is."
The Winter Soldier has been through a lot. Bucky Barnes began his career as an enlisted military man and eventually fought alongside Captain America as one of his elite Howling Commandos. It's not too hard to grasp what sort of military training Bucky had in his WWII career that affected his fighting style. But, from there, the Winter Soldier spent years as a brainwashed assassin for Hydra, where he picked up countless fighting styles to execute the goals of his sinister handlers.
An analysis of the Winter Soldier's fight scenes shows he knew Systema (most likely from his days as a Russian assassin), karate, boxing (from his 1940s war days with Captain America), and muay thai. This fight analysis showcased Bucky's boxing training through how he protected his face with his non-punching arm. Plus, it showcased his knowledge of Systema through his knife fight with Captain America, his ability to punch without twisting his body, and how he blocks kicks with a raised knee. Systema is a Russian fighting style that practically covers all aspects of combat, from punching to grappling, to knife fights, and even gunplay. Systema is also the most prominent style showcased by Bucky, which makes perfect sense considering the character's background as a Soviet-era assassin. Bucky is the Winter Soldier, after all.
The fight choreographer for Captain America: Civil War, as well as stunt double for Bucky, said he incorporated jeet kune do, boxing, sambo, and aikido as a basis for Bucky's style. Sambo especially goes hand in hand with Bucky's experience because it's a Russian martial art focused on grappling without weapons.
Peter Parker may not be traditionally trained in combat. Still, his spider abilities and Peter-tingle combined have caused him to innately use moves that belong to various fighting disciplines.
Much of Peter's fighting comes from his body's ability to perform incredible feats of gymnastics. As one fight analyst noted, Spider-Man uses Brazilian jiujitsu techniques to break out of holds. While Peter hasn't had any training, he is incredibly smart, so it seems as if he may just be devising moves on the fly with the knowledge of how the human body works and behaves. Peter also uses elements of tae kwon do, in that he often angles himself in ways that allow him to launch into strikes with his feet and legs. An element of professional wrestling is also in Peter's powers, as that's probably one of the only examples of fighting Peter has seen in his life, except unlike pro wrestlers, Peter has enough real-life strength to pull off those impossible moves in real life, utterly manhandling his opponents.
The best description of Peter's style is innate abilities paired with an incredible intellect. Peter has incredible powers with a brain that helps him figure out the best way to use them to his advantage.
Black Widow is the only Avenger known solely for their fighting style. Natasha Romanoff doesn't have superpowers or even a bow and arrow. What she does have is an insane proficiency in martial arts (and she occasionally has electric stingers on her wrists, but seriously, she's much more known for the countless times she has jumped on top of someone and brought them to the ground with her legs wrapped around their head).
The choreographer for Black Widow's fights, Jonathan Eusebio, said he "wanted to make Black Widow very fluid and acrobatic. Wushu, a Chinese fighting style, works well for her body mechanics." Black Widow is explosively fast and makes up for her small stature by using her entire body as a weapon. She effortlessly manages to flip off of one assailant before body-slamming onto another.
For the role of Thor, Chris Hemsworth trained in boxing and muay thai. The boxing influences are clear throughout all of Thor's appearances. Thor is a powerhouse, and he tends to deliver massive blows, whether that's with his hammer or fists.
Unlike characters like Black Widow or Spider-Man, Thor doesn't need to flip around to gain a good angle. Instead, Thor often just picks up the people he's fighting and throws them to the side. This sort of pickup-and-throw martial arts can be attributed to Glima, which works out perfectly for Thor as Glima is a Nordic fighting style.
