Non-thermal magnetospheric processes in the vicinity of supermassive black holes have attracted particular attention in recent times. Gap-type particle acceleration accompanied by curvature and Inverse Compton radiation could in principle lead to variable gamma-ray emission that may be detectable with current instruments. We shortly comment on the occurrence of magnetospheric gaps and the realisation of different potentials. The detection of rapid variability becomes most instructive by imposing a constraint on possible gap sizes, thereby limiting extractable gap powers and allowing to assess the plausibility of a magnetospheric origin. The relevance of this is discussed for the radio galaxies Cen A, M87 and IC 310. The detection of magnetospheric gamma-ray emission generally allows for a sensitive probe of the near-black-hole region and is thus of prime interest for advancing our understanding of the (astro)physics of extreme environments.