Unintegrated parton distributions and inclusive jet production at HERA

We describe how unintegrated parton distributions can be calculated from conventional integrated distributions. We extend and improve the last-step evolution approach, and explain why doubly unintegrated parton distributions are necessary. We generalise k(t)-factorisation to (z, k(t))-factorisation. We apply the formalism to inclusive jet production in deep-inelastic scattering, mainly at leading order, but we also study the extension to next-to-leading order. We compare the predictions with recent HERA data.