The backreaction problem for black holes in semiclassical gravity

Abstract The question of black hole evaporation is reviewed in the framework of quantum field theory in curved spacetimes and semiclassical gravity. We highlight the importance of taking backreaction effects into account to have a consistent picture of the fate of gravitational collapse in this framework. We describe the difficulties of solving the backreaction semiclassical equations due to practical complications of renormalizing the stress-energy tensor of quantum fields in general 3+1 spacetimes. We end with some personal views and plans on the subject.