  Although during the last decade new observations and new theoretical results
have brought better understanding of the physics of accretion onto compact
objects, many old and several new questions and problems await answers and
solutions. I show how the disc thermal-viscous instability model applied to
both cataclysmic variable stars and X-ray binary transients compels us to
conclude that assuming the existence in these systems of a flat accretion disc
extending down to the accretor's surface or to the last stable orbit and fed
with matter at its outer edge is too simple and inadequate a description of
these objects. It is also clear that, in most cases, these discs cannot driven
by (anomalous) viscosity only. The origin of the superhumps observed in
cataclysmic variables and X-ray binaries is, contrary to the common opinion,
still unknown. In accreting magnetic white dwarf systems outbursts not of the
dwarf-nova type can be due to the magnetic gating instability and/or
thermonuclear micronova explosions. Although the "typical" lightcvurves of
X-ray transients can be described by analytical formulae (but their decay phase
is not exponential), observations show that in many cases the light variations
in these systems are much more complex. An elementary argument shows the
impossibility of magnetars in pulsing ultraluminous X-ray systems, but we still
do not have a complete, self-consistent description of supercritical accretion
onto magnetized neutron stars and the resulting (necessarily beamed) emission.
Although it is (almost) universally believed that active galactic nuclei
contain accretion discs of the same type as those observed in binary systems,
the evidence supporting this alleged truth is slim and the structure of
accretion flows onto supermassive black holes is still to be determined.
