Pollicott--Ruelle resonances are the modes in expansions of correlations for Anosov (chaotic) flows. We show that they can be defined as limits of elliptic regularization of generators of the flow. In the case of contact flows we show that the resonance gap corresponding to exponential rate of mixing is independent of the regularization. (Joint work with S Dyatlov.) For any Anosov flow the essential gap is finite in the sense that there are always strips with infinitely many resonances. (Joint work with L Jin and F Naud.)