Due to the transverse device symmetry, the polarization properties of the light generated by surface-emitting semiconductor lasers will be strongly influenced by residual anisotropies. We describe the polarization dynamics of these lasers on the basis of a theoretical model founded on the coexistence of two different electron-hole recombination transitions, which give rise to circularly polarized fields with opposite helicities; the carrier densities available for these two transitions are coupled via spin-mixing processes. The residual cavity anisotropies are introduced in the model by means of the boundary conditions imposed to the counterpropagating fields: anisotropies which are symmetric and antisymmetric under time reversal will generate different boundary conditions. We include in the equations the effects of material strain, which causes symmetric linear phase and amplitude anisotropies, and of an externally applied magnetic field, which induces antisymmetric circular phase and amplitude anisotropies via the Faraday effect. This theoretical framework allows us to explain, with realistic values of the system parameters, some of the polarization behaviors exhibited by surface-emitting semiconductor lasers, namely, bistability and switching between orthogonal linearly polarized fields and magnetically induced ellipticity.