In this thesis we study two different aspects of holographic superconductivity. First we study fully backreacting Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. We explore the system’s dependence on the scalar mass for both positive and negative GB coupling, α. We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and α→(L^2)/4 the effect of backreaction is to increase the critical temperature, Tc , of the system: the opposite of its effect in the rest of parameter space. We also find that reducing α below zero increases Tc and that the effect of backreaction is diminished. We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. We investigate singular zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane. \ud \ud In the latter part of the thesis we investigate asymptotically anti de-Sitter (adS) and Lifshitz black holes in a bulk gravitational model that has a consistent embed-ding in string theory and that permits an arbitrary dynamical exponent, z ≥ 1. We find numerically that for both types of asymptotic spacetime there exists a two parameter family of black hole solutions. In the adS case these numerical solutions are supported by analytic solutions in the ‘probe’ or non-backreacting limit. Finally, we study the dependence of the black hole’s temperature on these two parameters
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