Asymptotically anti-de Sitter (AdS) spacetimes display intriguing phenomena which have recently sparked increasing interest in the research of gravitational solutions in these spaces. Considerable motivation stems from gauge/gravity duality, which is a conjecture relating classical gravity with a negative cosmological constant to strongly coupled quantum field theories. In this dissertation, we present novel stationary, asymptotically AdS black hole and soliton solutions, which we construct numerically. We employ numerical techniques which have been successfully used to tackle the complexities of the Einstein equations, and allow us to study the fully non-linear systems in unparalleled detail. We present a numerical study of rotating and charged hairy black hole solutions in five-dimensional AdS, which originate from a consistent truncation of $N=8$ supergravity, and can be uplifted to the type IIB supergravity with AdS$5\times$S$5$ asymptotics. The hairy black holes have one scalar field charged under a $U(1)$ gauge field, and branch from the near-extremal black holes due to the superradiant instability. We give numerical evidence that the hairy solutions exist arbitrarily close to the BPS bound for all charges, which is saturated in the zero and infinite temperature limits. We compute the phase diagram, and analyse the thermodynamics across different ensembles. Finally, we conjecture the existence of a one-parameter hairy solution extension of the known supersymetric black hole in this theory. Our work demonstrates the importance and complexity of black hole solutions with scalar condensate in supergravity. It also opens new possibilities to resolve a long-standing problem in Maldacena's original AdS/CFT correspondence, namely the understanding of the Bekenstein-Hawking entropy of supersymmetric black holes in terms of microstate counting. The study of gravitational solutions in AdS also provides valuable insights into classical phenomena in general relativity. In particular, superradiance has been important in the context of the weak cosmic censorship hypothesis. In order to study this relationship, we constructed novel four-dimensional asymptotically global AdS solutions by turning on a dipolar differential rotation at the conformal boundary. At fixed energy and boundary profile, we find two different geometries: a horizonless AdS soliton, and a deformed black hole. Both solutions develop an ergoregion attached to the boundary, and are superradiantly unstable. We discuss the intricate phase diagram which exhibits up to six-fold degeneracy, and the implications of our results for weak cosmic censorship and the corresponding dual field theory at strong coupling.