In practically every iteration of the character, Batman has been an undisputed master of martial arts. Setting superpowers aside, there aren't a lot of characters who can best Bruce Wayne in a straight hand-to-hand fight.
But what are the actual martial arts that Batman knows, and how did those skills evolve and develop over the years?
In the early days of the comics, Batman was an expert in boxing and wrestling. As Eastern martial arts began to gain mainstream recognition in the United States, Batman's character evolved to incorporate those techniques.
He was retconned to have also gained proficiency in disciplines like jujitsu (sometimes spelled as "jiu-jitsu," depending on the writer). The mention of Batman's background in these Japanese grappling arts first appeared in Detective Comics #36 in 1940, when the Caped Crusader escapes from a villain using an "old jiu-jitsu trick" (in the 40s, jiu-jitsu, jujitsu, and ju-jitsu all collectively referred to the Japanese martial art, not its Brazilian descendent that was gaining momentum in South America at the time).
However, due to an overall unfamiliarity with the subtleties of Japanese martial arts at the time, Batman's grappling techniques at the time more closely resembles jujitsu's cousin, judo. A kind of amorphous blend of the two martial arts was becoming more popular in the U.S. at the time, even being taught in the curriculum for various police forces.
Over the years though, as a fascination with all things "Oriental" grew in North America (due in large part to celebrities like Bruce Lee and Asian cinema in general), Batman's martial arts repertoire began to become more and more expansive.
Batman began to incorporate (at least in name) styles likes kung fu, aikido, karate, and many more. At one point in a fairly modern iteration of the character, Batman reveals he has learned techniques from 127 different martial arts disciplines.
Some of this training has been highlighted in the comics over the years. At various points in his life, Bruce Wayne trained with ninja in Japan, spent time with Zen warrior monks in the Himalayas, and studied under champion boxer Ted Grant.
Some writers have even pulled from more esoteric disciplines, like Dim-Mak and Yaw-Yan, to give Batman an even more expansive skill-set.
Though it's worth noting that, at times, various comic writers have downplayed Batman's martial arts background, with some going as far as to state that his combat aptitude was simply due to experience and just a general amount of badassery.
In more recent years, the cinematic versions of the character have taken a more realistic angle on Batman's fighting techniques.
In Batman Begins, Bruce Wayne is trained in ninjitsu-esque techniques by the League of Shadows. To give the character a fighting style that felt like it could work in real life though, the filmmakers turned to the Keysi Fighting Method, a system developed by martial artists and stuntmen Justo Dieguez and Andy Norman.
At its core, Keysi is designed to fight one or more opponents at the same time using a wide variety of upper-body striking techniques, utilizing not only punches, but also headbutts, elbows, and forearm strikes. There isn't a heavy priority placed on kicking, in order to maintain a strong base. It also incorporates techniques for dealing with armed assailants, which makes a lot of sense for the sort of situations that Batman often finds himself in.
In the comic and animated film The Dark Knight Returns, Batman shows off some Brazilian Jiu-Jitsu skills with a pretty solid armbar from the mount.
The Arkham video game series drew a lot of inspiration from aikido techniques, in particular in how Batman grapples with and disarms his opponents.
Most recently Ben Affleck's take on the character for Batman v Superman: Dawn of Justice even took inspiration from modern day mixed martial arts athletes.
"You kind of get a feeling like physical, visceral slugger thing. The fights are more like ... UFC-influenced. Like Conor McGregor style," he said in an interview.
Batman's martial art repertoire, like many aspects of comic books in general, have tended to reflect the zeitgeist and popular trends of the time. It's likely that we'll continue to see the Caped Crusader's fighting style evolve over time, as martial arts themselves are tested, refined, and improved upon.