Baxter Stockman's design and characterization have undergone significant physical, ethnic, and narrative transformations since his 1984 debut. Originally created by Kevin Eastman and Peter Laird as an African-American scientist in Mirage Studios' TMNT #2, his ethnicity was changed to Caucasian for the 1987 animated TV series. He was restored to an African-American character in the 2003 animated series and has consistently remained Black across all subsequent IDW comic continuities, animated shows, and live-action films. Physically, Stockman rarely remains purely human.

In the 1987, 2012, and animated film adaptations, he undergoes a horrific transformation into a giant humanoid fly known as Stockman-Fly. In contrast, the Mirage comic line and 2003 animated series depict a darker physical degradation where Shredder or his own failed experiments progressively dismember his body, reducing him to a cybernetic eye and brain inside robotic suits or a glass jar. Politically and narratively, Stockman evolved from a simple bank-robbing scientist into a master manipulator who successfully runs for office and becomes the Mayor of New York City in the IDW comic series.