In recent years we've greatly expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. While entanglement is very difficult to measure in experiments, it has nevertheless driven progress in 1) the classification of quantum phases of matter and 2) strategies for efficiently simulating many-body systems on classical and quantum computers. I will review some recent progress in these directions. Along the way I will summarise some older results on how entanglement grows in many-body systems, briefly highlight some connections to holography, and present a conjecture about the asymptotic computational difficulty of calculating transport in many-body systems.