  This article will summarize selected aspects of the semiclassical theory of
gravity, which involves a classical gravitational field coupled to quantum
matter fields. Among the issues which will be discussed are the role of quantum
effects in black hole physics and in cosmology, the effects of quantum
violations of the classical energy conditions, and inequalities which constrain
the extent of such violations. We will also examine the first steps beyond
semiclassical gravity, when the effects of spacetime geometry fluctuations
start to appear.
