The black hole stability problem is discussed in the context of recent progess in the study of linear wave equations on black hole backgrounds. In particular, I will suggest a new approach to a problem more intimately connected to the non-linear problem than the study of the scalar wave equation. In the second part I will present a proof of boundedness for the linear wave equation on Kerr-anti de Sitter spacetimes and a class of perturbations thereof. The result combines a novel Hardy inequality with redshift-techniques developed by Dafermos and Rodnianski.