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While parton showers are used ubiquitously in Monte-Carlo simulations of particle collisions, their theoretical accuracy has been the subject of extensive discussion in the last few years. The PanScales project aims to design parton showers that achieve higher accuracy than any of the standard tools used at present. In this talk, I will review the foundational principles behind our parton showers, and show results from parton showers accurate at next-to-leading logarithmic (NLL) level for e+e- colliders, deep inelastic scattering, and colour-singlet production in hadron-hadron collisions, and show the challenges involved to go beyond NLL.