  This dissertation elaborates on X-ray polarisation features of astrophysical
environments near accreting black holes. Although the work was originally
assigned to supermassive black holes in active galactic nuclei, the results are
also largely applicable to stellar-mass black holes in X-ray binary systems.
Several numerical models predicting the X-ray polarisation from these sources
are presented, including their immediate applications in the interpretation of
the latest discoveries achieved thanks to the Imaging X-ray Polarimetry
Explorer (IXPE) mission that began operating in December 2021. The modeling
ranges from radiative transfer effects in atmospheres of accretion discs to
general-relativistic signatures of X-rays travelling in vacuum near the central
black holes to reprocessing events in distant, circumnuclear components.
Various scales in physical and computational complexity are examined. A
unifying element of this dissertation is the focus on reflection of X-rays from
partially ionized matter.
