This review encompasses the fundamentals of kinetics of atom transfer radical polymerization (ATRP). ATRP is a versatile reversible-deactivation radical polymerization (RDRP) technique, frequently utilized to synthesize advanced functional materials. Detailed mechanistic investigations over the past two decades allowed for an in-depth understanding of the underlying processes and rational design of the reaction conditions. Various aspects of ATRP kinetics are reviewed such as initiation modes, methods allowing to decrease catalyst concentration, influence of the initiator, catalyst (transition metal, ligand, counterion), solvent, additives, type of monomer, and effect of temperature and pressure. Techniques utilized to determine kinetic parameters of catalytic systems are discussed. Finally, guidelines for synthesis of polymers with targeted architectures, predetermined molecular weights, narrow molecular weight distributions, and high retained chain end functionality are presented.