Measurements from the H1 and ZEUS collaborations of the diffractive deep-inelastic scattering process, ep -> eXY, where Y is a proton or a low mass proton excitation, are presented for photon virtualities in the range 2.2 < Q² < 1600 GeV² and squared four-momentum transfer at the proton vertex satisfying | t | < 1 GeV². Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis. Combining measurements of the inclusive diffractive deep-inelastic scattering process with an analysis of diffractive dijet production allows a very sensitive determination of both quark and gluon distributions.