Jet vetoes play an important role at the LHC in the study of the Higgs and the precise measurements of its properties. Experimental analyses often divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. In this talk I discuss the challenges of obtaining reliable theory predictions of cross sections with a jet veto and present a framework to carry out next-to-next-to-leading logarithmic resummation including next-to-next-to-leading order effects, while accounting for the action of the jet algorithm.