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This is a survey of recent progress in the structure and classificationtheory of nuclear C*-algebras. In particular, I outline how the UniversalCoefficient Theorem ensures a positive answer to the quasidiagonality questionin the presence of faithful traces. This has strong consequences for theregularity conjecture and the classification problem for separable, simple,nuclear C*-algebras. Moreover, it entails a positive solution to Rosenberg'sconjecture on quasidiagonality of reduced C*-algebras of discrete amenablegroups. This note is largely based on a joint paper with Aaron Tikuisis andStuart White.

QDQ vs. UCT