The existence of physics beyond the Standard Model (BSM) is well motivated from both experimental and theoretical points of view. However, data from the 7/8 /13 TeV LHC (Run I and early Run II) have ruled out new, electroweak-scale states that couple appreciably to the Standard Model. This suggests that new physics, if it is indeed accessible at the LHC, is likely (i) light and very weakly coupled or (ii) very heavy with sizable couplings. Interestingly, such mass scales correspond to regions of phase space for BSM collider processes where radiative corrections can be large, making necessary their resummation. We present examples of how QCD resummation can quantitatively and qualitatively change BSM phenomenology, particular for neutrino mass models, at the 13 TeV LHC and a prospective 100 TeV Very Large Hadron Collider.