Abstract: Asymptotically anti-de Sitter (aAdS) spacetimes have been intensively studied in recent years. Their timelike conformal boundaries are in causal contact with the interior of the spacetime, so one expects to have to specify boundary conditions on physical fields propagating in an aAdS background. I shall present a recent well-posedness result for the Klein-Gordon equation on general aAdS backgrounds, paying particular attention to the possible choices of boundary conditions. I shall also discuss the question of linear stability for stationary aAdS black-holes, and discuss how this is affected by boundary conditions.