  To describe Lifshitz and hyperscaling violating (HSV) phenomena in CM one
uses gauge fields on the gravity side which naturally realize the breaking of
Lorentz invariance. These gravity constructions often contain naked
singularities. In this thesis, we construct a resolution of the infra-red (IR)
singularity of the HSV background. The idea is to add squared curvature terms
to the Einstein-Maxwell dilaton action to build a flow from $\text{AdS}_4$ in
the ultra violate (UV) to an intermediating HSV region and then to an
$\text{AdS}_2 \times {\text{R}}^2$ region in the IR. This general solution is
free from the naked singularities and would be more appropriate for
applications of HSV in physical systems.
  We also study the Schwinger effect by using the AdS/CFT duality. We present
the phase diagrams of the Schwinger effect and also the "butterfly shaped-phase
diagrams" of the entanglement entropy for four different confining supergravity
backgrounds. Comparing different features of all of these diagrams could point
out to a potential relation between the Schwinger effect and the entanglement
entropy which could lead to a method of measuring entanglement entropy in the
laboratory.
  Finally, we study the "new massive gravity" theory and the different black
hole solutions it admits. We first present three different methods of
calculating the conserved charges. Then, by calculating the on-shell Gibbs free
energy we construct the Hawking-Page phase diagrams for different solutions in
two thermodynamical ensembles. As the massive gravity models are dual to
dissipating systems, studying the Hawking-Page diagrams could point out to
interesting results for the confinement-deconfinement phase transitions of the
dual boundary theories.
