The enormous contribution of Richard Feynman to modern physics is well known, both to teaching through his famous Feynman Lectures on Physics, and to research with his Feynman diagram approach to quantum field theory and his path integral formulation of quantum mechanics. Less well known perhaps is his long-standing interest in the physics of computation and this is the subject of this paper. Feynman lectured on computation at Caltech for most of the last decade of his life, first with John Hopfield and Carver Mead, and then with Gerry Sussman. The story of how these lectures came to be written up as the Feynman Lectures on Computation is briefly recounted. Feynman also discussed the fundamentals of computation with other legendary figures of the computer science and physics community such as Ed Fredkin, Rolf Landauer, Carver Mead, Marvin Minsky and John Wheeler. He was also instrumental in stimulating developments in both nanotechnology and quantum computing. During the 1980s Feynman re-visited long-standing interests both in parallel computing with Geoffrey Fox and Danny Hillis, and in reversible computation and quantum computing with Charles Bennett, Norman Margolus, Tom Toffoli and Wojciech Zurek. This paper records Feynman's links with the computational community and includes some reminiscences about his involvement with the fundamentals of computing.