"Many of the Higgs and new physics searches at the Large Hadron Collider involve signals with jets of energetic hadrons. This proposal will improve the theoretical predictions for such processes, focusing on three different aspects:1) Since backgrounds depend on the number of jets, search analyses are often separated into bins with a particular number of jets to improve sensitivity. I propose to improve the precision of these exclusive jet cross sections, through a next-to-next-to-leading logarithmic order calculation using the N-jettiness event shape. Improved predictions for the benchmark W+N jet process and the Higgs+N jet signal will be obtained in a form that is suitable for reweighting Monte Carlos. The latter is important for constraining the couplings of the observed new particle at the LHC, which will help establish whether it is the Higgs boson.2) Given the excellent performance of the ATLAS and CMS detectors at the LHC, there is an expanding interest in techniques that exploit the substructure of jets. I aim to obtain an analytic understanding of the behavior of jet substructure observables and test Monte Carlo simulations, which do not include higher order effects and are the most common tool for substructure analyses. Substructure observables that will be considered include: jet mass, jet charge, 3-subjettiness (relevant for boosted top quarks) and mass-drop/filtering. I propose to investigate the factorization and resummation of these techniques, as well as their calculation beyond the leading logarithmic accuracy of the Monte Carlo parton shower.3) I also proposes to calculate the collinear radiation in a jet at next-to-next-to-leading order, fully differential in the three body phase-space. This will be used to test at this order the exponentiation of logarithms from jet algorithms, which ""group"" the observed radiation into jets. These results are also an important ingredient in other higher-order calculations for processes with jets."