Recent developments in the spectropolarimetric study of compact objects, specifically black holes (stellar and massive) and neutron stars are reviewed. The lectures are organized around five topics: disks, jets, outflows, neutron stars and black holes. They emphasize physical mechanisms and are intended to bridge the gap between the fundamentals of polarimetry and the phenomenology of observed cosmic sources of polarized radiation, as covered by the other lecturers. There has been considerable recent progress in spectropolarimetry from radio through optical frequencies and this is producing some unique diagnostics of the physical conditions around compact objects. It is argued that there is a great need to develop a correspondingly sensitive polarimetric capability at ultraviolet through γ-ray energies.

Spectropolarimetric observations, particularly those at radio and optical wavelengths, have played an important role in high energy astrophysics. From the discovery of synchrotron radiation to the first good evidence for AGN unification, from the polarization patterns in the coherent emission of radio pulsars to the discovery of variable, linear polarization in the absorption troughs of broad absorption line quasars, polarization studies often provide the best and sometimes the only clue we have as to the geometric disposition of the emitting elements in these diverse sources when we cannot resolve them directly.

These notes summarize lectures delivered by Roger Blandford at the XII Canary Islands Winter School on Astrophysical Spectropolarimetry.