  Elliptical galaxies are generally luminous sources of X-ray radiation, and
contain large amounts of hot, interstellar gas. In the brighter X-ray galaxies,
the inferred masses of hot gas are consistent with those expected given the
present rates of stellar mass loss. The required rates of heating of the gas
are also roughly consistent with those expected from the motions of gas losing
stars. X-ray observations, particularly X-ray spectra, require a low rate of
Type Ia supernova heating and chemical enrichment in the gas. In the brightest
X-ray galaxies, the cooling times in the gas are short, which suggests that the
gas forms steady-state cooling flows. Steady cooling models explain most of the
properties of the brighter X-ray galaxies, including their luminosities, the
X-ray--optical correlation, their temperatures, and their surface brightness
profiles. Although the optical and X-ray luminosities of early-type galaxies
are strongly correlated, there is a large dispersion in this correlation. The
origin of the emission in the X-ray faint ellipticals is less certain. All
ellipticals appear to have a hard X-ray spectral component due to accreting
binary systems. X-ray faint ellipticals also have a very soft X-ray component,
which may be residual hot interstellar gas. The X-ray spectra of ellipticals
indicate that the abundance of iron is well below the solar value, which
implies that the rate of Type Ia supernova contamination is small. The
abundances and evidence for gradient gradients suggest that stellar abundance
gradients and inflow of the gas affect the X-ray spectra.
