Quantum chaotic dynamics manifests itself in transport, thermalization, and the butterfly effect. Hydrodynamics is the universal effective description of transport in the long distance, late time regime. We can gain insight into the process of thermalization from the time evolution of entanglement entropy, for which I introduce an effective theory valid in the hydrodynamic regime. I derive this theory in the special case of holographic gauge theories, and present strong evidence for its validity in any chaotic system. I discuss the interplay between this effective theory and chaotic operator growth that is responsible for the butterfly effect, and present new general results on the Lyapunov exponent characterizing this phenomenon. I conclude with some exciting implications for quantum gravity through gauge/gravity duality.