  Measurements of soft and hard diffractive processes have been performed at
the Tevatron p-pbar collider during the past decade. Diffractive events are
studied by means of identification of one or more rapidity gaps and/or a
leading antiproton. Here, results are discussed within the Tevatron data and
compared to those obtained at the HERA ep collider. The traditional ``pomeron''
is described within the framework of QCD and the issues discussed include
pomeron structure, diffractive cross section factorization, and universality of
rapidity gap formation. Exclusive dijet and low-mass state production in
double-pomeron exchange processes, including predictions for Higgs production
at the LHC from dijet measurements at the Tevatron.
