More than 250 years after establishing the electrical nature of the lightning flash, we still do not understand how a lightning channel advances. Most of these channels progress not continuously but in a series of sudden jumps and, as they jump, they emit bursts of energetic radiation. Despite increasingly accurate observations, there is no accepted explanation for this stepped progression.<br/><br/>This proposal addresses this open question. First, we propose a methodological breakthrough that will allow us to tackle the main bottleneck in the theoretical understanding of lightning: the wide disparity between length-scales within a lightning flash. We plan to apply techniques that have succeeded in other fields, such as multi-model coupled simulations and moving-mesh finite elements methods. Acting as a computational microscope, these techniques will reveal the small-scale electrodynamics around a lightning channel.<br/><br/>We will then apply these techniques to elucidate the intertwined problems of lightning channel stepping and thunderstorm-related high-energy emissions. The main hypothesis that we will test is that stepping is due to the formation of low-conductivity spots within the filamentary-discharge region that surrounds a lightning channel. This idea is motivated by observations from high-altitude atmospheric discharges. By resolving the small-scale dynamics, with our numerical method, we will also test hypothesis for high-energy emissions from the lighting channel, which crucially depend on the microscopic distribution of electric fields.<br/><br/>This interdisciplinary proposal, straddling between geophysics and gas discharge physics, seeks a double breakthrough: the methodological one of building multi-scale lightning simulations and the hypothesis-driven one of finding out the reason for stepping. If it succeeds, it will achieve a leap forward in our knowledge of lightning, undoubtedly one of the greatest spectacles in our planet's repertoire.