Special AT seminar by Fabian Kislat 7.7.2017 X-ray and gamma-ray imaging, spectroscopy and timing missions have revolutionized our understanding of compact astrophysical objects in the last few decades. Polarimetry promises qualitatively new insights by providing two new observables: the polarization fraction and angle. These new observables carry geometrical information about regions that are only pico-arcseconds across in the sky, too small to be imaged by any current or planned telescope, at any wavelength. In this talk, I will review the scientific potential of X-ray and gamma-ray polarimetry from sub-keV to MeV energies and provide an overview of the technical approaches covering this broad energy range. I will report on the 2016 flight of the balloon-borne hard X-ray polarimeter X-Calibur. Finally, I will conclude by giving an outlook to future funded and planned missions: the Imaging X-ray Polarimetry Explorer (IXPE), the X-ray Polarimetry Probe (XPP) concept, and the All-Sky Medium Energy Gamma-ray Observatory (AMEGO).