Vetoes on energetic jets are common in experimental analyses and are used to reject backgrounds which have similar final states to signal processes of interest. In placing a jet veto, however, one introduces a new scale into the theoretical calculation, which may be widely separated from the natural energy scale of the process. This induces large logarithms of the scale ratio at all orders in perturbation theory, which can spoil the convergence of a fixed order calculation. I will discuss the resummation of these logarithms in the framework of soft-collinear effective theory. After reviewing the treatment for colour singlet production, I will present a new factorisation theorem for Higgs boson production in association with a hard jet and show resummed results up to an approximate NNLL' accuracy. I will then discuss how resummed calculations of this kind can be used to construct a fully differential Monte Carlo event generator which matches NNLO calculations to a parton shower.