A gravitational perspective on strongly interacting quantum fields

This thesis aims to construct, refine and employ various holographic techniques to study phases of matter which typically lie outside of the reach of standard calculational frameworks. Armed with holography and guided by an intuition rooted in appeals to thermodynamic arguments, symmetries, constraints and approximate comparisons to other systems, we present a series of investigations intended to showcase holography's strength as a framework for modeling and contextualizing properties of a wide range of conventionally inaccessible phases of matter, with applications ranging from quantum phase transitions in metals to transport properties of the quark gluon plasma formed in heavy-ion collisions.