Recent developments in semiclassical gravity

Semiclassical gravity (SG) aims to describe the semiclassical regime of quantum gravity. In SG quantum fields curve classical spacetime in an effective way through the expectation value of their stress-energy tensor, while propagating in the spacetime they curve. I discuss some advances in SG in three directions: (i) in understanding structural properties or special solutions of SG in spacetimes with isometries or special Hadamard states (ii) in understanding the initial value formulation and (iii) in black hole evaporation and why information loss is not expected. Semiclassical frameworks beyond SG are briefly surveyed. The hope is that this short note will provide a good set of references and indicate interesting open problems and directions.