Temporal polarization instability is seen as an oscillatory or random variation in time of the polarization parameters of light interacting with a nonlinear system. Spatial polarization instability is the formation of ``frozen'' complex quasiperiodic or pseudochaotic distributions of the polarization parameters of a wave along the direction of propagation. The problem of polarization instability or multistability is intimately related to the polarization of eigenwaves in the nonlinear problem and their transformation as a result of ``hard'' and ``soft'' spontaneous polarization symmetry breaking. This paper presents a review of publications on polarization instabilities in passive nonlinear optical systems, including Fabry–Perot resonators, gyrotropic media, systems with strong two-photon absorption, birefringent crystals, fiber lightguides, and isotropic media.