In this talk, I will overview some recent developments in many-body quantum chaotic dynamics and its relation to quantum gravity. I will discuss how to characterize many-body quantum chaos using operator scrambling---the size growth of the support of an operator. I will describe the behavior of operator size in several different systems, including the Sachdev-Ye-Kitaev (SYK) model and quantum spin chains, and also discuss how to relate the operator size to experimental observables in quantum quench experiments. In the last part of the talk I will discuss the relation of operator size and holographic duality.
