  Viscous rotating accretion flows around black holes become
advection-dominated when the accretion rate $\dot M$ is sufficiently low. Most
of the accretion energy in such flows is stored within the gas and advected
radially inward. The temperature is therefore very high, and much of the
radiation comes out in hard X-rays and $\gamma$-rays. We have constructed an
advection-dominated accretion flow model for the Galactic Center source
Sagittarius A$^*$. The model consists of a $7\times10^5M_\odot$ black hole
accreting at $\dot M=1.2\times10^{-5}\alpha\, M_\odot{\rm yr^{-1}}$, where
$\alpha$ is the usual viscosity parameter. The model spectrum fits the
observations from radio to $\gamma$-rays quite well and explains the unusually
low luminosity of the source. Since the model explicitly makes use of a horizon
at the inner edge to swallow the advected energy, the success of the model
strongly suggests that the central object in Sgr A$^*$ is a black hole. We
further show that, if $\alpha$ is not much smaller than unity, then
advection-dominated models can be applied even to higher luminosity black
holes. The existence of Low and High States in black hole X-ray binaries, and
the abrupt transition between the two states, find a natural explanation. The
models also explain the close similarity in the hard X-ray/$\gamma$-ray spectra
of black hole X-ray binaries and active galactic nuclei.
