2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/5167I review our current theoretical understanding of the different possible rotating modes of accretion onto a black hole. I discuss both thick adiabatic flows and radiatively efficient thin disc solutions. I present a new self-consistent unified analytical description of two-phase thin disc--corona systems in which magneto-rotational instability is responsible for angular momentum transport in the disc and for the corona generation. Finally, I briefly discuss the role of magnetic fields in bridging the gap between accretion discs theory and jet production mechanisms10 pages, 1 colour figure. Latex macro sprocl.sty. Invited review, to be published in the proceedings of the 5th Italian AGN Meeting "Inflows, Outflows and Reprocessing around black holes" (2002)Astrophysicstext