Improving the accuracy of event generators

Parton showers are central to almost every collider analysis, but for a long time their formal accuracy was poorly understood. I will show how the PanScales collaboration has made shower accuracy something that can be systematically improved and tested. I will start with showers that reach next-to-leading-logarithmic (NLL) accuracy across a wide range of observables, and explain how we check that accuracy. I will then show the new considerations that arise at NNLL accuracy and discuss the new challenges when combining these with NNLO corrections.