In this talk I will discuss the impact of logarithms in s-hat/pt^2, so-called high-energy logs, on measurements of jet processes at the LHC. These logs slow the convergence of a standard fixed-order expansion in alpha_s, and furthermore, are enhanced by certain experimental cuts such as vector-boson-fusion cuts, vector-boson-scattering cuts or when searching for new physics at large m_jj. I’ll describe the High Energy Jets (HEJ) framework which provides new predictions at LL accuracy in a flexible Monte Carlo, and I’ll discuss their comparison to data. I’ll also describe the steps we’re taking towards NLL and recent work where the framework was extended to inclusive H+1j production (arXiv:2210.10671), the first process to be treated in this way which only requires one jet.