When the mass accretion rate onto a black hole (BH) falls below a critical rate, ˙(M)_crit_~α^2dot(M)_Edd_, accretion can occur via a hot optically thin flow where most of the dissipated energy is advected inward. We present such an advection-dominated model for the soft X-ray transient (SXT) A 0620-00. This source has a puzzlingly low X-ray luminosity in quiescence, ~6x10^30^erg/s, despite a relatively high mass accretion rate ~10^-10^Msun_/yr deduced from its optical flux. The accreting gas makes a transition from a standard thin disc at large radii to an advection-dominated flow at small radii. The transition occurs when the effective temperature of the thin disc is ~10^4^K. Because of the very low accretion efficiency, ~10^-3^-10^-4^, in the inner flow, the model fits both the optical and X-ray data. We also present models for V404 Cyg and Nova Mus 1991 in quiescence. Quiescent neutron star (NS) transients are expected to appear very different from BH systems because the advected energy is re-radiated from the NS surface whereas a BH swallows the advected energy. We discuss models for NS SXTs.