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.