In the past five years, quantum computational complexity has
become a thriving topic of research in the high-energy theory community due
to its relation to black hole interiors. I will describe these developments
in detail. In particular, I will discuss our progress toward understanding
complexity for quantum field theory states, both for pure and mixed 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.
