Quantum field theory in curved spacetimes is an extension of the standard quantum field theory to curved spacetimes. The theory studies the dynamics of quantum matter fields that propagate in static curved backgrounds. Thanks to the equivalence principle the quantization procedure closely resembles that of Minkowski spacetime once the proper formalism is chosen; however, interesting phenomena not present in flat spacetimes occur.
In generally curved spacetimes quantum fields lose its interpretation as particles. Only in certain situations, such as in assymptotically flat spacetimes, the notion of particle is recovered, and even when the particle interpretation holds the concept of particle depends on the observer. A general prediction of the theory is the creation of particles by gravitational fields.
Probably the most striking application of the theory of quantum fields in curved spacetime is Hawking's prediction that black holes radiate with a thermal spectrum. A related prediction is the Unruh effect: accelerated observers in the vacuum measure a thermal bath of particles.
The theory of quantum field theory in curved spacetime can be considered as a first approximation of the inaccessible theory of quantum gravity. A second step towards that theory would be semiclassical gravity, where the background is considered dynamic instead of being static (although it is still considered classical).