What can X-ray polarization tell us about accreting black hole systems?

With the launch of the Imaging X-ray Polarimetry Explorer (IXPE) by the year 2020/21, X-ray polarimetry will open a new window in astrophysics. Dedicated to high energy sources with sufficient X-ray luminosity, IXPE will target both stellar-mass black holes in binary systems and supermassive black holes in active galaxies. In this talk, I intend to review the main questions to be solved or constrained by X-ray polarimetry. I will show how polarimetric observations in the 2-8 keV band will measure the spin, disk inclination and mass of the black hole. Additional information about the surrounding medium, such as the amount of circumnuclear gas in active galactic nuclei (AGN) or the composition of outflowing polar winds will be derived simultaneously. By probing the iron Kalpha line band, X-ray polarimetry will also constrain the importance of General Relativity effects that are supposed to shape the spectra of pole-on objects. Finally, I will introduce how IXPE will map the Galactic Center in search of past activity.