Accretion onto compact objects plays a central role in high-energy astrophysics. The process of accretion can substantially affect the magnetic field strength and geometry (e.g, via the magneto-rotational instability or dynamo processes) and the accreting plasma density. The presence of the compact object itself can significantly affect the character and structure of the accreting plasma as well as its emission. This is especially true, in the case of an accreting black hole, when a significant fraction of the emission originates or passes near the horizon. To address this, we develop a manifestly covariant magnetoionic theory, capable of tracing rays in the geometric optics approximation through a magnetized plasma in a general relativistic environment. This is discussed for both the cold and warm, ion and pair plasmas. We also address the problem of performing polarized radiative transfer covariantly in these environments, considering in particular the anisotropic nature of magnetized plasmas, the gravitational redshift and Doppler shift, the transport of the polarization vector along the ray, and the ellipticity of the plasma eigenmodes. The presence of relativity qualitatively changes the dispersion relation, introducing a third branch. In addition it significantly augments various polarized emission and transfer effects in strongly sheared flows, such as jets. Additionally, we demonstrate that it is possible, due to refraction coupled with the existence of a horizon, to generate a net circular polarization regardless of the intrinsic polarization of the emission mechanism. We find that this is not likely to be of significant importance for circular polarization in AGN (including the Galactic center and M81). However, in the context of X-ray binaries, this may produce measurable circular polarizations in the infrared. We also develop a formalism for performing polarized radiative transfer through tangled magnetic fields. We find that for Faraday thick plasmas with a net magnetic helicity (but not necessarily a net magnetic field) it is possible to generate a circular polarization fraction which increases with frequency, as is observed to be the case in the Galactic center. In this case the handedness of the circular polarization is determined by the angular momentum of the accretion disk. This mechanism can be applied to extragalactic AGN and naturally explains the low degrees of circular polarization observed. As with the refractive mechanism, this may also be applied to X-ray binaries, and predicts ~10% polarization fractions at infrared wavelengths. Again, this provides a significant motivation for the development of infrared polarimetry.