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We give a review of results on superpolynomial decay of correlations, andpolynomial decay of correlations for nonuniformly expanding semiflows andnonuniformly hyperbolic flows. A self-contained proof is given for semiflows.Results for flows are stated without proof (the proofs are contained inseparate joint work with Balint and Butterley). Applications includeintermittent solenoidal flows, suspended Henon attractors, Lorenz attractors,and various Lorentz gas models including the infinite horizon Lorentz gas.

Superpolynomial and polynomial mixing for semiflows and flows