In the theory of general relativity, the dynamics of spacetimes are governed by the Einstein equations. These equations feature a real-valued constant, called the cosmological constant, the sign of which influences both local and global geometric properties of the spacetimes. Notably, when this constant is negative, the Cauchy problem for the Einstein equations must be treated as an initial boundary value problem and solutions are referred to as asymptotically Anti-de Sitter. In this talk, I will present the two known types of geometric boundary conditions leading to the local existence and uniqueness of such solutions: the Dirichlet boundary conditions, which were introduced by Friedrich in 1995, and the homogeneous Robin boundary conditions, which I introduced in a recent work.