Over the past 14 years, the Anti-de Sitter (AdS)/Conformal Field Theory (CFT) correspondence and its generalization in the ideas of gauge/gravity duality have had a profound impact in our understanding of strongly interacting quantum field theories. Roughly speaking, the correspondence maps the degrees of freedom of a $d$-dimensional quantum field theory in the strong coupling regime to weakly coupled string theory (gravity or supergravity) on a $(d+1)$-dimensional ``bulk" spacetime, enabling one to extract interesting information about the field theory spectrum and dynamics by performing relatively simple semi-classical calculations using standard general relativity techniques. Although much of the original progress in the field was driven by applications to formal supersymmetric gauge theory or by the desire to construct gravitational systems whose field theory duals resemble different phases of Quantum Chromodynamics (QCD), in recent years the scope of the AdS/CFT correspondence has grown to encompass interesting systems in condensed matter and atomic physics, including phenomena such as superconductivity and superfluidity, non-relativistic scale invariance, quantum criticality and others. In this thesis we present several applications of gauge/gravity duality techniques to the study of such systems, some of them from a phenomenological perspective, where an textit{ad hoc} gravitational theory is devised to model particular phenomena, and some from a string-theoretical perspective, where the gravitational system is embedded in the framework of string or M-theory. In particular, we describe studies of quantum criticality in $(2+1)$-dimensional field theories at finite charge density via extremal four-dimensional black holes, the modeling of systems with non-relativistic scale-invariance and broken time-translation invariance (``Aging" phenomena), and the coupling of fermions to holographic superconductors in $(2+1)$ and $(3+1)$ dimensions from explicit embeddings in type IIB string theory and M-theory.