Linearly polarized radiation in the hard X-ray/soft gamma-ray band is expected from a large variety of astronomical sources. We discuss the importance of polarimetric studies for several classes of sources-pulsars, accreting black holes, magnetic neutron stars and jets from active galaxies-and then describe PoGOLite, a balloon-borne instrument which is currently under construction and will be able to measure the polarization of electromagnetic radiation from such extra-solar objects in the energy range 25-80 keV.