  I 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 mechanisms
