Jet vetoes are regularly used in LHC searches to separate signal from background, for example in Higgs decays to WW. To draw conclusions about signal cross sections, we need to know the jet veto efficiency with some accuracy. This talk will start by examining why the determination of jet veto efficiencies has been the subject of intense discussion recently. It will then go on to explain the progress that has been made in applying QCD resummation techniques to this type of problem and show how this improves our predictions for Higgs studies.