I will describe recent progress in the study of chaos in complex and highly entangled quantum systems. Building on the rich history of quantum chaos, this recent activity is driven by new experimental possibilities and by a remarkable convergence of ideas in many-body physics, quantum information, and gravity. The focus will be on the quantum butterfly effect and its relation to the spreading of entanglement and to emergent speed limits. I will also describe how this physics is being probed in experiments. Finally, I will present a candidate for a universal effective field theory of many-body chaos based on the concept of operator size.