From Queenpedia.com

Queen's next single was their first collaboration with another artist outside of their solo work. Recorded by chance when they were all working at Mountain Studios, in Montreux, Queen and David Bowie worked on two songs together, 'Cool Cat' (which later emerged on the band's 'Hot Space' album minus Bowie's backing vocals) and 'Under Pressure' - a jam based loosely on an existing song the band had worked on in demo form. The result was a #1 smash in the UK, and became an immediate live favourite in Queen's reppertoire, even if Bowie himself felt the song could have been much better.

Both artists were unavailable to record a promotional video due to touring commitments, David Mallet was asked to come up with something suitable. Taking the theme of pressure, Mallet edited together stock footage of traffic jams, commuter trains packed with passengers, explosions, riots, cars being crushed and various pieces of footage from silent films of the 1920s, most notably influential Sergei Eisenstein's Soviet film 'Battleship Potemkin' and Fritz Lang's chilling 'Nosferatu', a master work of the German Expressionist movement which also spawned 'Metropolis', a film that would later be strongly connected with the band.

Serving as a chilling reminder of mankind's constant desire to detroy one another, and at the same time love and have fun (there is also footage of crowds enjoying concerts, and lots of black and white kissing scenes), the video remains a powerful collage to this day. Two versions currently exist, as 'Top Of The Pops' refused to broadcast the original edit because it contained footage of explosions in Northern Ireland. The more well known version featured on both 'Greatest Flix II' and 'Greatest Video Hits 2'.