Modelled on the Anti-de Sitter space, asymptotically Anti-de Sitter spaces can be defined as Lorentzian manifolds that possess a timelike conformal boundary. Due to their lack of global hyperbolicity, finding asymptotically Anti-de Sitter solutions to the Einstein equations (necessarily with a negative cosmological constant) through the Cauchy problem requires tackling the latter as an initial boundary value problem. In this talk, I will present the two known types of geometric boundary conditions leading to the local existence and uniqueness of solutions in dimension 4: the Dirichlet boundary conditions, which were introduced by Friedrich in 1995, and the homogeneous Robin boundary conditions, which I introduced in a recent work.