The title comes from the main character's name, Axel Foley (played by Eddie Murphy), in the film.
Faltermeyer recorded the song using five instruments: a Roland Jupiter-8 provided the distinctive "supersaw" lead sound, a Moog modular synthesizer 15 provided the bass, a Roland JX-3P provided chord stabs, a Yamaha DX7 was used for bell and marimba sounds and a LinnDrum was used for drum programming.
In addition to the Beverly Hills Cop soundtrack, the song also appears on Faltermeyer's 1988 album Harold F. as a bonus track. Reportedly, Faltermeyer was against including it, but MCA insisted as it was his most recognizable track. It was also used for the official starting lineup song of the Pasig Blue Pirates (later Pasig-Rizal Pirates) of the Metropolitan Basketball Association in the late 1990s.
It has become a pop culture staple, being redone by such artists as "Crazy Frog" and referenced by such shows as "Family Guy".