This book is a comprehensive description of hybrid plasma simulation models and will provide a very useful summary and guide to the vast literature on this topic. It addresses researchers and graduate students knowledgeable about computational science and numerical analysis, and can be used in courses on astrophysical and space plasmas. It is also meant for plasma installation designers. The coupled Vlasov--Maxwell equations with collisions describing well the physical system are far too heavy for numerical siumulations. Hybrid models treat some aspects kinetically and some as fluids. In the first part the author discusses hybrid codes, which include a wide spectrum of description for ions, positrons, dust grains, atoms and electrons. In the second part he treats the applications to basic plasma phenomena like particle acceleration and dissipation processes as well as to the global interaction of the solar wind with nonmagnetic planets, comets, and the local interstellar medium.