We describe the second SIGMORPHON shared task on unsupervised morphology: the goal of the SIGMORPHON 2021 Shared Task on Unsupervised Morphological Paradigm Clustering is to cluster word types from a raw text corpus into paradigms. To this end, we release corpora for 5 development and 9 test languages, as well as gold partial paradigms for evaluation. We receive 14 submissions from 4 teams that follow different strategies, and the best performing system is based on adaptor grammars. Results vary significantly across languages. However, all systems are outperformed by a supervised lemmatizer, implying that there is still room for improvement.