[en] Jet vetoes play an important role at the LHC in the search for the Higgs and ultimately in precise measurements of its properties. Many Higgs analyses divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. For a given jet category, the veto on additional jets introduces sensitivity to soft and collinear emissions, which causes logarithms in the perturbative expansion that need to be resummed to obtain precise predictions. We study the higher-order resummation properties of several conceptually distinct kinematic variables that can be used to veto jets in hadronic collisions. We consider two inclusive variables, the scalar sum over p_T and beam thrust, and two corresponding exclusive variables based on jet algorithms, namely the largest p_T and largest beam thrust of a jet. The inclusive variables can in principle be resummed to higher orders. We show that for the jet-based variables, there are dual effects due to clustering in the jet algorithm for both large and small jet radius R that inhibit a complete resummation at or beyond next-to-leading logarithmic order (NLL). For R∝1, the clustering of soft and collinear emissions gives O(1) contributions starting at NNLL that are not reproduced by an all-order soft-collinear factorization formula and therefore cannot be resummed by it. For R<<1, clustering induces logarithms of R that contribute at NLL in the exponent of the cross section, which cannot be resummed with currently available methods. We explicitly compute the leading jet clustering effects at O(α²_s) and comment on their numerical size.