Roche tomography is a technique designed for mapping the intensity distribution over the surface of binary star components that fill (or nearly fill) their Roche lobes and so are both rotationally and tidally distorted. It builds on and develops the successful techniques used for mapping rapidly rotating single stars, which have revealed the presence of starspots. It has so far been applied to only a small number of cataclysmic variables, and a few other related systems. This paper reviews the technique and presents maps of spots on most of these systems. The review has been written with the help of contributions of material from Chris Watson and Colin Hill of Queen's University, Belfast.