We have developed an effective field theory framework to account for multiple scales in scattering processes, addressing additional scales that are due to: performing multiple measurements on the same final state, hierarchies between jet energies or angles, the size of the jet, jet grooming techniques that are used to remove contamination, etc. Highlighting two important applications we studied: Higgs plus jet production at the LHC, and the groomed momentum sharing variable. The latter has been measured extensively, as it probes fundamental properties of quarks and gluons. Our calculations take their theoretical description to the next level. There were also surprises during this project: for example, we discovered that a novel jet definition leads to considerable simplifications in (and thereby much more precise) theoretical calculations. We proposed using this as a new way of measuring the three-dimensional structure of the proton using jets, that could play an important role at the future Electron-Ion Collider.