In this thesis we exploit various tools to investigate aspects of black hole microstate geometries within the context of the “fuzzball proposal”, which follows from the string theory construction of black holes in terms of strings and branes. This thesis comprises three parts. In Part I, we make use of the gauge-gravity duality to discuss the precision holographic dictionary, that relates the asymptotic expansion of black hole microstates near the AdS boundary with the expectation values of certain operators in the dual CFT. In particular, we derive the dictionary for scalar chiral primary operators of dimension two and a class of superdescendants of these operators, in the single-particle basis. In Part II, we construct the first family of three-charge supersymmetric solutions containing a shockwave and we give a proposal for their holographic duals, which passes non-trivial checks. These gravitational solutions do not represent a single pure state in gravity: they provide a collective description of a family of microstates whose details are not resolved in supergravity. In Part III, we use computer science tools to derive approximate examples of microstate geometries. In particular, we present an optimization algorithm, based on evolutionary algorithm and Bayesian optimization, to construct numerical multi-center solutions with a high number of centers in generic configurations. The research conducted in this thesis supports the ideas of the fuzzball paradigm, and develops techniques which can prove useful to examine and test the conjecture in future scenarios.