In my talk, I want to present our results for the NNNLO zero-jettiness soft function in perturbative QCD, the last ingredient required for
fully-differential description of hadronic color-singlet production, production of two jets in e+e- annihilation, and single jet production in deep inelastic scattering via zero-jettiness as a slicing variable, the current frontier of modern colliders precision predictions. The complexity of calculations with the jettiness variable required the development of new approaches to reduction and calculation of phase-space integrals with theta-function constraints. The reduction of such integrals with real emissions and virtual corrections, as well as the construction of differential equations and their solution for master integrals, will also be discussed in my talk.