The music is by Jack Nitzsche and Ry Cooder. There are also songs (like Mick Jagger's fantastic Memo To Turner) but they were all recorded specially for the movie (I think!). Great mix of blues, funk, soul and trippy eastern psych influences.
The soundtrack to Robert Altman's 'Kansas City'. It's a so-so film, not Altman's best, but it has a great performance by Harry Belafonte as a super-sinister mobster. The film is set in the Kansas City of Altman's youth, specifically in the Hey Hey club, where they have a houseband made up of the hottest local jazz stars of the day. Altman hired the best players he could find in '96 when the film was made, and had them re-create the sound of Kansas City in the 30s, going to great lengths to record the sessions live in the studio. The musicians involved included Olu Dara, Joshua Redman, James Carter, Don Byron, Geri Allen, Ron Carter, Christian McBride, etc - a truly stellar line-up. I've raved about this album here before, but it bears repeating: if you have even a passing interest in jazz, this album is a great hidden gem. The sound quality is superb, the playing just about as good as it gets, the tunes are classics, and the whole thing swings like hell.