Accretion onto black holes often proceeds via an accretion disc or a temporary disc-like pattern. Variability features, observed in the light curves of such objects, and theoretical models of accretion flows suggest that accretion discs are inhomogeneous and nonaxisymmetric. Fast orbital motion of the individual clumps can modulate the observed signal. If the emission from these clumps is partially polarized, which is probably the case, then rapid polarization changes of the observed signal are expected as a result of general relativity (GR) effects.

In this contribution we will summarize the expected effects in terms of the model of bright orbiting spots. As the signal from accreting black holes peaks in X-rays, the polarimetry in this spectral band will be particularly useful to examine the strong-gravity effects that should modulate the signal originating near the horizon. We will mention similarities as well as differences between the manifestation of GR polarization change in X-rays and in other spectral bands, such as the infrared region, where the polarization measurements of the radiation flares from the immediate vicinity of the horizon are currently available and can be used to probe the Sagittarius A* supermassive black hole in the Galactic Centre.