This book describes the rich and diverse realm of accreting binary systems, made up of a compact object such as a white dwarf, neutron star or black hole, orbiting a companion star. It details the nature, formation and evolution of accreting binaries, describing how extensive observations, accompanied by simulations, allow astronomers to better understand the energetic phenomena occurring in these intriguing systems. The book also describes how multi-messenger astronomy is currently revolutionizing our view of these systems, adding gravitational waves, neutrinos and cosmic rays to the photon light we receive from them. Aimed at graduate students and researchers, this book provides an introduction to the topic, first describing the astrophysical basics of both single and binary stars, before moving on to detail the different types of accreting binary systems such as cataclysmic variables (CVs), low-and high-mass X-ray binaries (LMXBs/HMXBs), and peculiar binaries such as intermediate-mass X-ray binaries (IMXBs) and ultraluminous X-ray sources (ULXs), finishing up with a panorama of multimessenger research.