Understanding the microscopic structure of black holes and, more generally, of arbitrary spacetime regions, is one of the fundamental problems of quantum gravity. The holographic principle suggests that the information content of a spacetime region is encoded in degrees of freedom on the boundary of that region. To this aim, progress in AdS/CFT suggests that the emergence of spacetime from boundary degrees of freedom entails a deep connection between gravity and entanglement. In this thesis, we attempt to gain insight into this problem by following two different approaches. A particularly important step towards understanding the emergence of spacetime is explaining the origin of black hole entropy. Given that black holes are subregions of spacetime, a ``bottom-up'' approach to black hole entropy would first require understanding the gravitational degrees of freedom on the boundaries of subregions, at both the classical and quantum levels. A particularly powerful way to shed light on these degrees of freedom is by characterizing the symmetries and charges of gravitational theories with internal boundaries. In the first part of this thesis, we primarily focus on this question at the classical level. We start by considering subregions behind causal horizons, which we treat as null boundaries of the spacetime. We then extend the analysis to causal diamonds. We apply this formalism to event horizons, using the algebra of charges to derive the entropy of a black hole. Lastly, we study the measurability of gravitational charges at asymptotic boundaries when quantum corrections are included. While the first part of this thesis focuses on the purely gravitational aspects of black holes and spacetime, the second part aims to uncover the profound relationship between these concepts and quantum field theory (QFT). The classic example of this is the quantum null energy condition (QNEC), a novel inequality in quantum field theory relating energy and entanglement which was discovered through the classical focusing theorem in general relativity. We first study the relationship between the QNEC and quantum focusing using AdS/CFT. We then study the QNEC purely using QFT, and show that it is always saturated, which displays a deep connection between energy and entanglement. We also use black hole entropy to derive energy-minimizing states in QFT which are naturally understood in terms of modular flow. Finally, we derive the holographic dual of this modular flow.