Magnetism in binary stars is now an area of central importance in stellar astrophysics. Magnetic fields are believed to play a fundamental role in the mass transfer process in all close binaries. After an outline of the early work in binary stars, the book introduces the fundamentals of magnetohydrodynamics and binary star theory. The main areas of MHD in binary stars are then considered, including the AM Herculis systems, intermediate polars, X-ray binary pulsars, accretion disc magnetism, and stellar and disc winds. The unifying theme is the property of magnetic fields of redistributing angular momentum, and the associated stellar spin evolution. Although this is a rapidly expanding area, the fundamental problems discussed here are likely to remain relevant for future decades. A knowledge of physics to undergraduate level is assumed. The material should be of interest to observers as well as theoreticians. Although the book is mainly aimed at research workers, parts of the text could be useful for postgraduate courses in astrophysical fluid dynamics and binary star theory.