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Parton shower event generators are essential tools for establishing the quantitative connection between theory and experiment. However, their flexibility comes with a trade-off: they generally offer lower formal accuracy compared to state-of-the-art analytic calculations, which in turn have more limited applicability. The poor accuracy of the inevitably employed parton shower generators introduces systematic uncertainties that affect all measurements at colliders. In this talk, I will discuss the efforts made by the PanScales collaboration to improve the logarithmic accuracy of parton showers, focusing on the recently achieved NNLL accuracy for event-shapes. Until a few years ago, this accuracy was limited to leading logarithms. During the last few years NLL accurate parton showers have emerged, and very recently it has been shown how to improve them one logarithmic order further in the soft sector. This advance, combined with analytic understanding of event-shape resummation, has allowed us to construct the first parton shower with NNLL accuracy for global event-shapes, next-to-single non-global logarithmic (NSL) accuracy, and next-to-next-to-double-logarithmic (NNDL) accuracy for jet multiplicities. These developments are crucial for refining our understanding of fundamental particle interactions and reducing uncertainties in present and future collider measurements.