  Black holes and weakly-magnetic accreting neutron stars show strong
quasi-periodic variability over timescales that span a very wide range. This
property offer us a unique opportunity to improve our understanding of basic
physical processes in strong gravitational fields as it reveals, for the first
time, phenomena that occur on the most fundamental timescales near accreting
compact objects. In this article, I review our current understanding of the
variability properties of accretion flows onto neutron stars and black holes. I
discuss a number of challenges faced by theoretical models, in order to
identify open questions in accretion physics that need to be addressed.
Finally, I discuss the relation to and implications for variability models of
the detection of nearly coherent oscillations during type I X-ray bursts in
several neutron-star sources.
