A systematic review is made of the experimental and theoretical investigations of the mechanism and kinetics of mass transfer in a system of islands of substance A deposited on a solid substrate of substance B in which A is insoluble. The analysis is carried out on the assumption that the total amount of matter present jointly in the islands and in a two-dimensional gas of adsorbed atoms is constant. Behavior of systems of islands at rest and in motion is discussed. Coalescence of islands is considered in the case of diffusive mass transfer between islands at rest and also in the case of direct collisions between moving islands. ``Dispersion hardening'' of the surface by a system of islands, which hinders evaporation and growth of a crystal, is described. Considerable attention is devoted to reporting experimental investigations carried out mainly by electron microscopy. Some new effects are predicted, including a possible phase transition during coalescence of islands, size effect in recrystallization, one-dimensional coalescence, etc.