In this presentation, I will discuss the tremendous progress in high-precision simulations for the Large Hadron Collider (LHC) in the past few years. The focus will be on the inclusion of next-to-next-to-leading-order perturbative corrections in parton-shower generators (NNLO+PS). After mentioning the existing NNLO+PS methods, I will present highlights of phenomenological results obtained with the so-called MiNNLO approach. Such precision simulations have applications beyond the LHC. Besides their impact
on future colliders, such as the currently most likely programme of an FCC-ee,an application to accurately model the prompt neutrino background for neutrino telescopes (e.g. ICECUBE) will be presented. Finally, I will introduce a novel idea to include higher-order corrections in event simulations through a recursive approach.