Accretion discs are an important component of many diverse astrophysical
systems, ranging from AGNs to protostellar discs. In this talk I am going
to discuss the influence of accretion disc instabilities in the overall
evolution of such systems. In the first part of my talk I am going to
focus on gravitational instabilities that may arise when the disc mass is
a sizable fraction of the central objects mass (either a supermassive
black hole or a young protostar). I will show how these instabilities can
be very effective in transporting angular momentum in the disc, thereby
promoting the accretion process. I will also discuss the issue of
fragmentation of a massive disc, describing the details and the
likelihood of this process. In the second part of the talk I am going to
concentrate on warping disturbances, describing their propagation
properties and eventually focusing on the Bardeen-Petterson effect,
discussing how the disc can align (or misalign) with the spin of the
central supermassive black hole.