One of the goals of quantum information theory is to understand quantum systems from the standpoint of computational complexity. How difficult is it to compute fundamental properties of a quantum system or simulate a particular system over time? A central idea in understanding these questions is quantum entanglement. On one hand, entanglement is a valuable resource that enables quantum computation and communication. On the other hand, the fact that some quantum systems have bounded entanglement accounts for the success of certain computational methods in finding ground states and simulating dynamics. I will give an overview of recent work in understanding the complexity of ground states of quantum systems both from the perspective of computational complexity and from the perspective of quantifying entanglement.