Few-shot classification refers to learning a classifier for new classes given only a few examples. While a plethora of models have emerged to tackle it, we find the procedure and datasets that are used to assess their progress lacking. To address this limitation, we propose Meta-Dataset: a new benchmark for training and evaluating models that is large-scale, consists of diverse datasets, and presents more realistic tasks. We experiment with popular baselines and meta-learners on Meta-Dataset, along with a competitive method that we propose. We analyze performance as a function of various characteristics of test tasks and examine the models' ability to leverage diverse training sources for improving their generalization. We also propose a new set of baselines for quantifying the benefit of meta-learning in Meta-Dataset. Our extensive experimentation has uncovered important research challenges and we hope to inspire work in these directions.