This review covers the basic principles of surface-initiated atom transfer radical polymerization (SI-ATRP). SI-ATRP is a robust and versatile method for preparation of various hybrid materials with controlled molecular characteristics of the tethered polymer chains, such as polymer composition and architecture. Various aspects of SI-ATRP, such as polymer brush grafting density, surface geometry, and reaction conditions, including structure of initiator, ligand, and catalyst, are important for engineering the structure and properties of the hybrid polymer materials. Elementary reactions, such as initiation, propagation, termination, transfer, and activation/deactivation equilibria as well as factors affecting these processes are discussed. The properties of materials prepared by SI-ATRP are illustrated through several selected examples.