In this talk I will discuss the high-energy logarithms which appear when the centre-of-mass energy of a QCD collision is much larger than the transverse momenta of the observed jets. Several factorised expressions are required to bring this study to next-to-next-to-leading logarithmic (NNLL) accuracy. As a step in this direction, we have recently obtained a one-loop factorised expression in N=4 SYM for the central emission of two gluons. I will highlight some novel features of this expression compared to what has been seen at NLL accuracy. We will then turn our attention to the LHC and consider the impact of these high-energy logarithms. I will describe the High Energy Jets (HEJ) framework, which includes the dominant high-energy logarithms to provide all-order predictions for several relevant LHC processes including Higgs, W, or Z boson production in association with at least two jets. I will highlight recent progress in matching the HEJ framework to NLO accuracy (arXiv:2012.10310).