  As the luminosity of an accreting black hole drops to a few percent of
Eddington, the spectrum switches from the familiar soft state to a hard state
that is well-described by a distended and tenuous advection-dominated accretion
flow (ADAF). An ADAF is a poor radiator, and the ion temperature can approach
10^{12} K near the center, although the electrons are cooler, with their
temperature typically capped at ~10^{9-11} K. The foundational papers predicted
that the large thermal energy in an ADAF would drive strong winds and jets, as
later observed and also confirmed in computer simulations. Of chief interest,
however, is the accreting gas that races inward. It carries the bulk of the
accretion energy as stored thermal energy, which vanishes without a trace as
the gas passes through the hole's event horizon. One thus expects black holes
in the ADAF regime to be unusually faint. Indeed, this is confirmed by a
comparison of accreting stellar-mass black holes and neutron stars, which
reside in very similar transient X-ray binary systems. The black holes are on
average observed to be fainter by a factor of ~100-1000. The natural
explanation is that a neutron star must radiate the advected thermal energy
from its surface, whereas a black hole can hide the energy behind its event
horizon. The case for an event horizon in Sagittarius A*, which is immune to
caveats on jet outflows and is furthermore independent of the ADAF model, is
especially compelling. These two lines of evidence for event horizons are
impervious to counterarguments that invoke strong gravity or exotic stars.
