Radiative corrections of quantum electrodynamics cause a vacuum threaded by magnetic field to be birefringent. This means that radiation of different polarizations travels at different speeds... Even in the strong magnetic fields of astrophysical sources the difference in speed is small; however, it has profound consequences for the extent of polarization expected from strongly magnetized sources. We demonstrate how the birefringence arises from first principles, show how birefringence affects the polarization state of radiation and present recent calculations for the expected polarization from magnetars and X-ray pulsars. (read more)