I will discuss recent stability and instability results for the linearised Einstein equations around Kerr-adS spacetimes. In the Schwarzschild-adS case, I will present a stability result with weak inverse logarithmic decay, a rate which we show is sharp by a quasimodes construction (joint work with Gustav Holzegel). In the Kerr-adS case, I will present mode stability results below the Hawking-Reall bound (joint work with Gustav Holzegel) and mode instability results above the Hawking-Reall bound.