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Supernovae are among the most powerful and influential explosions in theuniverse. They are also ideal multi-messenger laboratories to study extremeastrophysics. However, many fundamental properties of supernovae related totheir diverse progenitor systems and explosion mechanisms remain poorlyconstrained. Here we outline how late-time spectroscopic observations obtainedduring the nebular phase (several months to years after explosion), madepossible with the next generation of Extremely Large Telescopes, willfacilitate transformational science opportunities and rapidly accelerate thecommunity towards our goal of achieving a complete understanding of supernovaexplosions. We highlight specific examples of how complementary GMT and TMTinstrumentation will enable high fidelity spectroscopy from which the lineprofiles and luminosities of elements tracing mass loss and ejecta can be usedto extract kinematic and chemical information with unprecedented detail, forhundreds of objects. This will provide uniquely powerful constraints on theevolutionary phases stars may experience approaching a supernova explosion; thesubsequent explosion dynamics; their nucleosynthesis yields; and the formationof compact objects that may act as central engines.

Achieving Transformative Understanding of Extreme Stellar Explosions with ELT-enabled Late-time Spectroscopy