This survey is devoted to the current state of theoretical studies of two-dimensional dipole systems. Systems of hydroxyl groups on the surfaces of oxides have been the most experimentally studied systems. The article examines the orientational states of isolated radicals in local potentials of hindered rotation, various types of orientational ordering of dipoles in twodimensional lattices, and the appearance of the dipole glass phase in a system with arbitrary filling of lattice sites by particles. Proof is presented of the existence of long-range order in twodimensional dipole systems, as well as estimates of phase transition temperatures. There is a discussion of the theory of the vibrational spectra of ordered and disordered systems of dipole radicals in various orientational phases. Experimental data are presented on the infrared spectroscopy of surface hydroxyl groups. The data verify theoretical results. Unresolved problems are indicated as well as the prospects for further studies of two-dimensional dipole systems.