This thesis discusses two separate questions within the field of gauge/gravity dualities. The first is what is the gravity dual of a CFT state and it is based on work done in collaboration with my advisor, Prof. Skenderis, and which was presented in [1]. In particular, we develop a systematic perturbative construction of bulk solutions that are dual to CFT excited states. The second question concerns four dimensional theories that admit charged planar AdS black hole solutions carrying axionic charge and which can support additional scalar hair. More specifically, we discuss a number of analytic solutions in which the axions have a linear profile in the boundary directions and the additional scalar field satisfies mixed boundary conditions. We focus on the effect of these features on the thermodynamics and dynamic stability of the solutions and we use our results to study phase transitions between solutions with the same asymptotic charges and which satisfy the same boundary conditions. These results are based on work done in collaboration with M. Caldarelli, I. Papadimitriou and K. Skenderis and which was presented in [2].