Abstract: I will give an overview of results on asymptotically anti-de Sitter (aAdS) spacetimes in the mathematical community. I will discuss the issue of (in)stability and existence of time periodic solutions and then focus on recent joint work with Arick Shao (arXiv:2207.14217) addressing the question in what form the metric and the stress tensor on the conformal boundary determine (locally) the infilling aAdS spacetime.