Published online by Cambridge University Press: 12 April 2016
Recent work on advection-dominated accretion flows (ADAFs) is reviewed. The article concentrates on an optically thin branch of ADAFs which is present at mass accretion rates below a critical value ~ (10−2 – 10−1) the Eddington rate. Models based on this branch have been quite successful at explaining a number of low-luminosity X-ray binaries and galactic nuclei, and some brighter systems. Some progress has also been made toward understanding the various spectral states of accreting black holes. It is argued that ADAFs may provide one of the best techniques for demonstrating the reality of event horizons in black holes.