This paper presents XLS-R, a large-scale model for cross-lingual speech representation learning based on wav2vec 2.0. We train models with up to 2B parameters on nearly half a million hours of publicly available speech audio in 128 languages, an order of magnitude more public data than the largest known prior work. Our evaluation covers a wide range of tasks, domains, data regimes and languages, both high and low-resource. On the CoVoST-2 speech translation benchmark, we improve the previous state of the art by an average of 7.4 BLEU over 21 translation directions into English. For speech recognition, XLS-R improves over the best known prior work on BABEL, MLS, CommonVoice as well as VoxPopuli, lowering error rates by 14-34% relative on average. XLS-R also sets a new state of the art on VoxLingua107 language identification. Moreover, we show that with sufficient model size, cross-lingual pretraining can outperform English-only pretraining when translating English speech into other languages, a setting which favors monolingual pretraining. We hope XLS-R can help to improve speech processing tasks for many more languages of the world.