We present several results on scattering by Kerr-de Sitter slowly rotating black hole. In particular, we show that the scattering resolvent is meromorphic in the entire complex plane; its poles are known in astrophysics as quasi-normal modes, and in scattering theory as resonances. We then study the distribution of quasi-normal modes, establishing a resonance free strip and comparing our asymptotic results with the numerics done by physicists. As an application, we prove that linear waves on Kerr-de Sitter metric decay exponentially in a certain compact set.