From the Wikipedia entry:
"Coming Up" was the punchy lead-off track from Paul McCartney's McCartney II album, released in 1980. Like the rest of the album, the song had a minimalist synth feel to it, and featured humorously processed vocals from McCartney.
Another version of the song was recorded in concert in 1979. This version, taped in Glasgow, Scotland, had a much fuller sound, and later hit number one on the U.S. Billboard Hot 100, despite being released as the single's b-side track to the studio version. In one of his last interviews, John Lennon was complimentary on this song. It was McCartney's final hit during Lennon's lifetime.
"Coming Up" is also well known for its video, using electronic trickery, a band consisting of McCartney dressed up as other famous pop music stars playing the other instruments - the stars honored in such a way include Buddy Holly, Neil Young, Ron Mael of Sparks, Ginger Baker of Cream, and he also appears as Beatle Paul in his early 1960s stage dress.