Abstract: Collider experiments will achieve percent level precision measurements of several processes key to answer some of the most pressing questions of contemporary particle physics. In this talk I will show that the capability to predict and describe such observables at next-to-next-to-next-to-leading order (N3LO) in QCD perturbation theory is crucial to fully exploit these experimental measurements. I will describe how to compute differential distributions via EFT-based subtraction methods and illustrate the calculation of the N3LO TMD and N-jettiness beam functions. These constitute the last missing ingredients for extending these techniques to N3LO for processes such as Higgs production in gluon fusion and Drell-Yan, and a key element for the application of these techniques toprocesseswith jets in the final state at this order. Finally, I will present the determination of the rapidity anomalous dimension (Collins-Soper kernel) to N4LO. I will employ it to carry out the resummation of the Energy-Energy Correlation at N4LL (the first resummation for an event shape observable at this level of accuracy) and discuss its application to obtain predictions beyond N3LO for LHC processes.