We review some of the properties of advection-dominated accretion flow (ADA
F) models and show that they successfully describe many astrophysical syste
ms. Despite these successful applications some fundamental problems still r
emain to be solved, the most important one being the physics of the transit
ion between an ADAF and a geometrically thin Keplerian disc. (C) 1999 Elsev
ier Science B.V. All rights reserved.