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Introduced by Schubert in the early nineties, the spaces of pseudo-stable curves provide modular compactifications for the spaces of smooth curves. In contrast to the usual Deligne-Mumford compactifications by stable curves, pseudo-stability allows the curves to have both nodal and cuspidal singularities, but disallows elliptic tails. In this talk, I'll discuss recent and ongoing work that aims to better understand the tautological intersection ring of the spaces of pseudo-stable curves.