Holographic Duality postulates the equivalence between certain quantum gravity theories and non-gravitational quantum field theories in a space of fewer dimensions. In particular, string theory on an asymptotically anti-de Sitter spacetime is equivalent to a Conformal Field Theory on a different spacetime. This duality has proven to be a useful tool in the study of some strongly-coupled systems. Recent progress suggests that entanglement plays a crucial role in the emergence of spacetime and gravity from the degrees of freedom of the quantum field theory. In this talk I will give an overview of these ideas, and describe some progress related to holographic entanglement entropy in time-dependent problems.