Motivated by problems in data clustering, we establish general conditions\nunder which families of nonparametric mixture models are identifiable, by\nintroducing a novel framework involving clustering overfitted \\emph{parametric}\n(i.e. misspecified) mixture models. These identifiability conditions generalize\nexisting conditions in the literature, and are flexible enough to include for\nexample mixtures of Gaussian mixtures. In contrast to the recent literature on\nestimating nonparametric mixtures, we allow for general nonparametric mixture\ncomponents, and instead impose regularity assumptions on the underlying mixing\nmeasure. As our primary application, we apply these results to partition-based\nclustering, generalizing the notion of a Bayes optimal partition from classical\nparametric model-based clustering to nonparametric settings. Furthermore, this\nframework is constructive so that it yields a practical algorithm for learning\nidentified mixtures, which is illustrated through several examples on real\ndata. The key conceptual device in the analysis is the convex, metric geometry\nof probability measures on metric spaces and its connection to the Wasserstein\nconvergence of mixing measures. The result is a flexible framework for\nnonparametric clustering with formal consistency guarantees.\n