String theory with certain asymptotically AdS boundary conditions can be defined non-perturbatively using the AdS/CFT correspondence, which reformulates the theory in terms of a non-gravitational quantum field theory in a lower dimensional spacetime. In this way many of the subtleties of quantizing gravity are circumvented, however, the price of this simplification is that locality is no longer manifest, even in an approximate sense. In this dissertation we study features of asymptotically AdS spacetimes related to causality and search for these properties in the dual CFT description. We begin by reviewing some of the salient features of the correspondence and studying some puzzles related to the Ryu-Takayanagi conjecture. We then show that the notion of boundary causality associated with the Gao-Wald theorem implies that holographic CFT's on Minkowski space must satisfy the averaged null energy condition (ANEC). The ANEC is a quasilocal energy condition that requires the integrated null energy on a null line to be positive. Any violations of this condition in a holographic theory would result in "causal shortcuts'' through the bulk spacetime which would allow propagation outside of the light cone in the CFT. We next study causal wedges associated with subregions of the boundary and argue that these regions of the bulk spacetime are associated with a particular coarse-graining of the CFT reduced density matrix. In particular, we conjecture that the area of the codimension-two boundary of these wedges is equal to a particular coarse-grained entropy which we name the 'one-point entropy.' We present several suggestive examples in which the conjecture holds as well as a proof that it holds to leading order in a class of spacetimes with a bulk first law. In an appendix we explain how the conjecture is equivalent to a statement about the classical Einstein equation which in principle could be rigorously proven or falsified.