On the Complexity of Black Holes

In the last few years, quantum computational complexity from quantum information theory has become a thriving topic of research in the high-energy community due to its relationship to black holes. This relation stems from the AdS/CFT correspondence, which relates the properties of quantum field theories to those of gravitational systems. I will describe these recent developments in detail and comment on our recent progress in defining complexity in quantum field theory and in studying the relevant dual gravitational observables. I will comment on implications of these ideas to studying the interior of black holes and on the relation to the information paradox.