The circular polarization of the Cosmic Microwave Background (CMB) is usually taken to be zero since it is not generated by Thomson scattering. In this talk I will discuss possible methods of generating circular polarization in the CMB due to propagation effects. I will only consider physics inside the Standard Model. I will present two classes of mechanisms for birefringence: alignment of matter to produce an anisotropic susceptibility tensor, and anisotropy of the radiation field coupled to the non-linear response of the medium to electromagnetic fields; this can occur either via photon-photon scattering (non-linear response of the vacuum); atomic hyperpolarizability (non-linear response of neutral atoms); or plasma delay (non-linear response of free electrons). The strongest effect comes from photon-photon scattering from recombination. Nevertheless, our results are consistent with a negligible circular polarization of the CMB in comparison with the linear polarization or the sensitivity of current and near-term experiments.