The current state of experimental and theoretical research into cooperative phenomena in crystals containing off-center ions is reviewed. This field has attracted considerable attention in recent years because of the general interest in disordered systems, including spin glasses of which dipole glass is the electric analog. The properties of dipole glass in alkali halide crystals containing off-center ions are discussed. Experimental studies performed over the last few years have shown that off-center ions can induce the ferroelectric phase transition in highly-polarizable crystals. The physical nature and the theory of the phenomenon are examined, and the physical properties of crystals exhibiting this induced phase transition are discussed. Possible lines of future research into cooperative phenomena in crystals containing off-center ions are reviewed.