Baker received his B.A. in film studies from New York University. His first feature film was Four Letter Words, a film revolving around the look of views, attitudes and language of young men in America; Baker wrote and directed the film, and also edited it. Baker then went on to make Take Out, which was co-written, co-directed, co-edited and co-produced by Baker himself and Shih-Ching Tsou, The film revolves around an illegal Chinese immigrant falling behind on payments on a smuggling debt, leaving him only one day to come up with the money. The film had its world premiere at the Slamdance Film Festival on January 18, 2004, and took five years before the film was released in a limited release by CAVU Pictures on June 6, 2008. Baker then created Greg The Bunny, a sitcom; Baker directed it and also wrote episodes for the series, the series originally aired on Fox before being moved to IFC, and it lasted three seasons. Baker's third feature film Prince of Broadway premiered at the Los Angeles Film Festival on June 22, 2008. The film revolves around a New York street hustler who makes profit by creating name-brand knock offs, to only discover he has a son he never thought he had, it was released in a limited release on September 3, 2010 in a limited release. Shortly after, Baker, Spencer Chinoy and Dan Milano created a spin-off to Greg The Bunny called Warren the Ape; the series aired on MTV and was canceled after one season. Baker's fourth feature, Starlet, starred Dree Hemingway and Besedka Johnson, had its world premiere at SXSW on March 11, 2012. The film was released in a limited release on November 9, 2012. Baker's fifth feature, Tangerine, was shot completely on an iPhone 5S and featured Kitana Kiki Rodriguez, Mya Taylor, Karren Karagulian, Mickey O'Hagan and James Ransone and was executive produced by Mark Duplass, and Jay Duplass. The film had its world premiere at the 2015 Sundance Film Festival on January 23, 2015. The film was released in a limited release on July 10, 2015.