Rex Edward Richards was born in Colyton, Devon in 1922. He was educated at the local grammar school and St John's College, Oxford. He graduated with First Class Honours in 1945 and undertook research on infrared spectroscopy with H.W. (later Sir Harold) Thompson, obtaining his D.Phil. in 1948. In 1947 he was elected a Fellow and Tutor in Chemistry at Lincoln College and in 1964 succeeded Sir Cyril Hinshelwood as Dr Lee's Professor of Chemistry. He became Warden of Merton College in 1969 when he transferred his research to the Department of Biochemistry. He served as the Vice Chancellor of Oxford University for the period 1977-1981. In 1984 Richards gave up both the Warden's Lodgings and the research laboratory to become Director of the Leverhulme Trust. From 1982 to 1998 he was Chancellor of Exeter University.

Richards's research focussed on nuclear magnetic resonance (NMR) spectroscopy. He was one of the early workers in the field after the war and has been at the forefront of the application of NMR techniques to chemical problems and a leader in the design and development of NMR equipment. In the 1960s he became interested in biological applications of NMR, a change of direction facilitated by the move to the Biochemistry Department and the development of new NMR instruments using super-conducting magnets. In 1969 (the year of the move to Biochemistry) Richards and a number of colleagues from eight scientific departments formed the Oxford Enzyme Group, a consortium of researchers from different disciplines who agreed to contribute a significant part of their research effort to a collaborative venture. Richards was the chairman of the Enzyme Group from its beginning until 1984.

Richards's scientific achievements have been recognised with numerous honours and awards. In 1954 he received the Corday-Morgan Medal of the Chemical Society and in 1977 the Chemical Society Award in Theoretical Chemistry and Spectroscopy. He was elected a Fellow of the Royal Society in 1959 and awarded its Davy Medal in 1976, and a Royal Medal in 1986. He received a Knighthood in the Queen's Jubilee Honours List in 1977.