The specific features of relaxation kinetics in systems with different kinds of confinements are discussed in the paper. In contrast to the usual Arrhenius, Eyring, or Vogel-Fulcher-Tammann patterns, a quite unusual nonmonotonic dependence of relaxation time versus temperature is observed in such systems. Based on the free volume concept, a model for this type of kinetics was illustrated by several particular examples: water conlined in porous glasses and in zeolites, confined liquid crystals, doped ferroelectric crystals, and heteropolymer folding.