After Hawking showed that quantum field theory in curved spacetime (without reference to the Einstein field equations) predicted that a black hole formed by collapse will emit thermal radiation, it became clear that there is an unexpected connection between spacetime geometry (Killing horizons) and thermal effects for quantum fields. In particular, there is a very general relationship between thermal radiation and spacetimes that admit a one-parameter group of isometries possessing a bifurcate Killing horizon, which consists of a pair of intersecting null hypersurfaces that are orthogonal to the Killing field.