Supermassive black holes power accretion flows and outflows, and resulting radiation is observed at different wavelengths. A significant energy fraction of these flows may be carried by cosmic rays and associated high-energy non-thermal radiations. Recently, associations of high-energy neutrinos with galaxies hosting supermassive black holes, active galactic nuclei and tidal disruption events, have been reported. We review the implications of the multimessenger data for theoretical models and discuss their challenges. We highlight the importance of the current and future neutrino and gamma-ray telescopes to probe non-thermal phenomena in the vicinity of supermassive black holes.