John Papaloizou has made fundamental theoretical studies of the structure and stability of a wide variety of astrophysical systems, including galaxies, stars, accretion discs and protoplanetary discs. His discovery with James Pringle that accretion tori can be dynamically unstable is central to understanding the role of such tori in powering quasars. He and Philip Palmer explained the radial orbit instability in anisotropic stellar systems. He and his collaborators have elucidated many aspects of the behaviour of close binary stars, including warped accretion discs, toroidal stellar oscillations, and apsidal motion.