Vickers graduated from King's College, Cambridge with a degree in mathematics, he then read a PhD at Leeds University also in mathematics.

In 1980 he started working for Nine Tiles which had previously written the Sinclair BASIC for the ZX80. He was responsible for the adaptation of the 4K ZX80 ROM into the 8K ROM used in the ZX81 and also wrote the ZX81 manual. He then wrote most of the ZX Spectrum ROM, and assisted with the user documentation.

Vickers left in 1982 to form "Rainbow Computing Co." with Richard Altwasser. The company became Jupiter Cantab and they were together responsible for the development of the commercially unsuccessful Jupiter ACE, a competitor to the similar Sinclair ZX Spectrum.

Originally at the Department of Computing at Imperial College London, Steve Vickers later joined the Department of Pure Mathematics at the Open University before finally moving to the School of Computer Science at the University of Birmingham. He is currently a Senior Lecturer and the Research Student Tutor of the School of Computer Science at the University of Birmingham.

Vickers' main interest lies within geometric logic. He has written over 30 papers in scholarly journals on mathematical aspects of computer science, and a book, Topology via Logic (Cambridge University Press, 1996, ISBN 0521576512).