In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In this context, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time. In this talk, I will present a proof of this conjecture in the setting of the spherically symmetric Einstein-massless Vlasov system, and also discuss some more recent results regarding other related problems.