We report recent results on diffraction from the CDF experiment at the Fermilab Tevatron ${\bar p}p$ collider. In events with multiple rapidity gaps, we find that if a single gap survives, \eg is not killed by products of interactions between spectator partons, any additional gaps survive as well. Diffractive structure functions are studied in single-diffractive and double-pomeron-exchange (DPE) dijet production. Exclusive production of dijets and of $\chi_{ c}^0$ in DPE have been studied as benchmark processes for exclusive Higgs production at the LHC.

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