Holography remains one of the most powerful approaches to understanding quantum gravity. The currently best-understood realization of holography is AdS/CFT -- a map between a quantum gravity theory in anti-de Sitter space (AdS) and a conformal field theory (CFT) on its boundary. In this thesis, several aspects of this duality are explored, with a focus on entanglement, chaos and causality. Entanglement plays an especially important role in holography because it is deeply connected to the emergence of spacetime; chaos is another key player in recent developments of holography because it is a characteristic feature of black holes that is expected to persist beyond the classical regime; finally, the idea of causality is a valued concept even in a quantum theory of gravity where the spacetime itself fluctuates, and the boundary CFT which has a well-defined notion of causality is a pragmatic starting point for understanding causality in a bulk theory of quantum gravity. One main theme of the thesis is to explore how these aspects depend on the theory. In particular, conclusions are drawn for whether certain statements that hold in General Relativity hold in general higher-derivative gravity and/or with higher-spin fields. Another theme is the connections between different concepts. In particular, boundary quantities that are apparently very different may be intricately related from the bulk perspective.

This dissertation investigates thermal holographic quantum field theories dual to gravitational systems with black holes. This study has relevance for experimental physics in a lab or near an astrophysical black hole as well as for the structure of higher dimensional quantum field theories. The dissertation begins with an introduction to AdS/CFT, entanglement entropy, and numerical methods.

The next two chapters explore constraints on holographic quantum field theories with a semi-classical dual. In chapter two, a scalar field is used to construct an ``extended wormhole'' that connects two identical asymptotic regions and is globally static. Mutual information of identical regions in the two boundary CFTs show that the expanded throat corresponds to rapid thermalization in the field theory. In the third chapter, a finite temperature phase transition in the gravitational path integral is used to constrain the spectrum of charged, spinning operators in the dual thermal CFT.

The fourth and fifth chapters are concerned with the study of thermal quantum field theories around black holes. In chapter four, the holographic dual of a zero-temperature quantum field theory on a finite temperature Reissner-Nordstr{\"o}m black hole background is constructed. The entanglement entropy of annular regions in the field theory explains a phenomenon called ``jamming,'' in which heat flow is impeded due to strong interactions. In chapter five, the holographic dual to a quantum field theory on the interior of a doubly-spinning Myers-Perry black hole is constructed. The null energy along the Cauchy horizon diverges negatively, indicating singular behavior and providing evidence for strong cosmic censorship.

The sixth chapter constructs the holographic dual to a strongly interacting metal with charged bosonic excitations. Such a field theory is a candidate system to describe the pseudogap phase of the high temperature superconductors. Experiments on these systems exhibit a metal-insulator transition at zero temperature and power-law conductivities at low temperature. On the gravity side, a domain wall potential for a scalar field interpolates between UV and IR conformally invariant spacetimes with different length scales. The dimension of the scalar controls the temperature and frequency dependence of the low temperature conductivity.

Holographic dualities like AdS/CFT provide a non-perturbative definition of a bulk theory of quantum gravity in terms of a lower-dimensional boundary quantum field theory. Elucidating quantum gravity thus becomes the challenge of deciphering the dictionary between bulk and boundary physics, and using it to translate basic properties of the latter into lessons about the former. A crucial intermediary between these two realms is the gravitational path integral, which defines the bulk theory in terms of an integral over spacetimes subject to conditions from the boundary theory. Though shallowly understood and rather formal, this piece of technology has thus far been able to provide deep insights into quantum gravity. This thesis is organized in three parts, each focusing on a different basic property in quantum theory and its consequences for quantum gravity through the gravitational path integral: entanglement, causality, and factorization.

Part I addresses the emergence of spacetime from entanglement, with a focus on understanding constraints on the entanglement structure of quantum states to posses classical geometries as holographic bulk duals. These constraints can be expressed as linear inequalities and used to define the holographic entropy cone (HEC). A systematic study of the HEC is accomplished by reformulating the holographic computation of von Neumann entropies as a graph-theoretic one, thereby recasting a complicated problem in differential geometry as a purely combinatorial one. This allows to prove important properties of the HEC, devise proof methods and algorithms for constructing it, derive precise relations to other polytope structures, and ultimately pursue a top-down understanding of the HEC from the universal quantum inequality of subadditivity. This part concludes with an exploration of how the machinery involved in the study of the HEC may also be generalized to settings where the von Neumann entropy receives contributions from bulk quantum fields, a regime where the graph-theoretic apparatus has to be upgraded.

Part II presents an alternative perspective on spacetime emergence, both in classical and quantum regimes, based on causality. Starting at a classical level, we explain how the conformal bulk geometry can be reconstructed by encoding its causal structure in data accessible from the boundary field theory. Through the use of field theory correlators, we propose a method for obtaining the full-dimensional bulk geometry up to a conformal factor. This generalizes the approach to bulk metric reconstruction based on light-cone cuts to a prescription which allows for recovering even those dimensions which become compact asymptotically. Moving away from the classical limit, we then resolve a known puzzle that arises from a tension between the bulk and boundary causal structures when the bulk theory is understood as a genuine gravitational path integral over spacetimes.

Finally, part III delves into the consequences of the lack of factorization that occurs in holography when wormholes are included in the gravitational path integral. In particular, we study generating functionals in quantum gravity and propose a recipe for their computation which accounts for the contribution of such connected topologies. This allows to differentiate between quenched and annealed quantities in quantum gravity, a distinction which may be used as a consistency test-ground for foundational aspects of the gravitational path integral regarding summing over topologies.

This thesis is divided into three Parts. In Part I the general theory of black holes in higher dimensions is discussed. In addition to an introductory essay, two studies of linear perturbations of Myers-Perry black holes are presented. These black holes are the higher dimensional generalization of the Kerr black hole, and their analysis reveals numerous instabilities. Threshold unstable modes provide the connection between the Myers-Perry black holes and novel stationary black hole solutions such as black rings or black Saturns, as well as other non-stationary solutions known as single Killing vector field black holes.

In Part II gauge/gravity duality is briefly reviewed and two aspects are studied in detail. First, the problem of finding a holographic dual to a superconductor with d-wave order parameter is investigated, and second, we examine the problem of holographic thermalization in field theories dual to rotating black holes.

Lastly, in Part III the role of de Sitter solutions in string theory is discussed. A recent puzzle surrounding the fate of the de Sitter landscape is reviewed, and it is shown how the study of black holes in certain flux backgrounds can provide insight into this puzzle. We then present a theorem ruling out the addition of black holes to a certain class of flux backgrounds. Finally, a study is presented which shows that black holes can be added to the flux backgrounds relevant for the de Sitter landscape in string theory, thereby providing strong evidence for the resolution of the puzzle.