We present a systematic study of propagation of circularly polarized beams in a Kerr medium. In contrast to previous studies, vectorial effects (i.e., coupling to the axial component of the electric field and the grad-div term) and nonparaxiality are not neglected in the derivation. This leads to a system of equations that takes into account nonparaxiality, vectorial effects, and coupling to the opposite circular component (i.e., the one rotating in the opposite direction). Using this system we show that the standard model in the literature for self-focusing of circularly polarized beams can lead to completely wrong results, that circular polarization is stable during self-focusing, and that nonparaxiality and vectorial effects arrest collapse, leading instead to focusing-defocusing oscillations. We also show that circularly polarized beams are much less likely to undergo multiple filamentation than linearly polarized beams.