Callis was educated at the Edinburgh College of Art. The band played many gigs in Edinburgh and Glasgow, during which Callis wore space suits and other hi-tech costumes. He was a member of The Knutsford Dominators before forming The Rezillos in 1976. He wrote the Rezillos' 1978 hit "Top of the Pops". In late 1978, after the release of the band's only album, The Rezillos split in two, with Callis forming Shake along with Simon Templar (born Simon Bloomfield) and Angel Paterson. Shake released two singles before splitting, with Callis later joining Boots for Dancing.
Callis released a solo single, "Woah Yeah!", in 1981 on the pop:Aural label, and also joined The Human League, playing both keyboards and lead guitar and making contributions as a backing vocalist. Callis co-wrote many tracks and following his departure from the band in 1986, he has returned several times either to play keyboard, or to offer help with songwriting. He co-wrote the band's 1990 hit Heart Like a Wheel together with former Rezillos band mate Eugene Reynolds. The track was produced by Martin Rushent.