Abstract. 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 developments in detail. In particular, I will discuss our progress towards understanding complexity for quantum field theory states and the study of the relevant dual gravitational observables. I will explain the implications of these ideas on studying the interior of black holes.