Traditional clustering algorithms such as K-means rely heavily on the nature of the chosen metric or data representation. To get meaningful clusters, these representations need to be tailored to the downstream task (e.g. cluster photos by object category, cluster faces by identity). Therefore, we frame clustering as a meta-learning task, few-shot clustering, which allows us to specify how to cluster the data at the meta-training level, despite the clustering algorithm itself being unsupervised. We propose Centroid Networks, a simple and efficient few-shot clustering method based on learning representations which are tailored both to the task to solve and to its internal clustering module. We also introduce unsupervised few-shot classification, which is conceptually similar to few-shot clustering, but is strictly harder than supervised* few-shot classification and therefore allows direct comparison with existing supervised few-shot classification methods. On Omniglot and miniImageNet, our method achieves accuracy competitive with popular supervised few-shot classification algorithms, despite using *no labels* from the support set. We also show performance competitive with state-of-the-art learning-to-cluster methods.