Degenerate stellar objects are expected to be strong sources of polarized X-ray emission. This is particularly true for strongly magnetized neutron stars, e.g. accretion or rotation powered pulsars, and gamma ray bursters. In these, linear polarization degrees well in excess of 30 percent are expected. Weaker magnetic field stellar sources, such as old neutron stars in low mass binary systems, white dwarfs and black holes are expected to have polarization degrees in the range 1-3 percent. A great interest attaches to the detection of polarization in these objects, since this would provide invaluable information concerning the geometry, radiation mechanism and magnetic field strength, necessary for testing and proving models of the structure and evolution of stars in their late stages. In this paper we review the theoretical models of the production of polarized radiation in compact stellar X-ray sources, and discuss the possibility of detecting these properties using currently planned detectors to be flown in space.