I review the basic physical processes that determine the evolution of accretion discs. I first introduce the main properties of discs observed around young stars across the mass spectrum. I then turn to the analysis of the fundamental disc equations, highlighting several subtleties, in some cases rarely discussed in textbooks. I then discuss some classic accretion disc solutions, both steady state and time dependent. I emphasise the description of the outbursting FU Orionis objects, the class of protostellar objects best suited to investigating the accretion process. I discuss in some detail the possible physical mechanisms responsible for transport in accretion discs, with particular emphasis on gravitational instabilities, which are rarely discussed in this context.