This book offers an updated comprehensive review of the rapidly expanding field of GRMHD simulations. In Part I, it reviews the basic equations for GRMHD simulations and for numerical relativity. Part II describes public codes for GRMHD simulations. Part III is devoted to accretion processes onto compact objects in the non-self-gravitating fluid approximation. Part IV reviews the state of the art of GRMHD simulations with self-gravitating fluids. This book represents both a valuable book for graduate students and important reference resource for researchers in the field.