Alex Cox was born in Bebington, Wirral, Nr. Liverpool, Merseyside. Cox studied at Wirral Grammar School and later at Worcester College, Oxford, then embarked upon a course in film studies at Bristol University and UCLA in California.

As well as directing films, Cox helped pen a rejected screenplay for the film version of Fear and Loathing in Las Vegas. He has also written on the subject of film for publications such as Sight and Sound, The Guardian, The Independent, and Film Comment.

From 1988 to 1994, he presented the television series Moviedrome on BBC Two, providing introductions to a series of alternative or obscure films that would otherwise be unknown to the general public.

As a film aficionado, Cox also lent his opinions to numerous film documentaries, and provided introductions for ITV4's Spaghetti Western series made by Free@Last TV and directed by Katie Kinnaird. He has also provided introductions to DVDs such as the BFI edition of Kurosawa's Red Beard and Eureka Video's release of Kaneto Shindo's Onibaba. In June 2008 he introduced the films in BBC Four's Western Weekend.

During his career, Cox has turned down offers to direct the films Robocop, Three Amigos, and The Running Man. Following his success with Repo Man, Cox had planned to direct a semi-sequel in the mid-90s, entitled Waldo's Hawaiian Holiday, in which he intended to star Emilio Estevez, Harry Dean Stanton, Rebecca De Mornay, and Willem Dafoe.

However, funding was never established, but in April 2008 it was released as a graphic novel. The script is available for download at alexcox.com. In 1996, De Mornay co-produced The Winner, with results Cox disowns, referring to the released version as his Alan Smithee film.