Recent observations have strengthened the dynamical arguments for the presence of black holes in X-ray binary systems, the Galactic center and the nuclei of the majority of bright galaxies. They have also drawn attention to the fact that accretion does not always proceed in the simple, stationary manner envisaged in early theories. I wish to discuss four related topics that are relevant to understanding the behavior of accreting black holes. (In view of the length constraints imposed by conference proceedings I shall make no attempt to give adequate bibliographic references for what follows.)