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NLP is currently dominated by general-purpose pretrained language models like RoBERTa, which achieve strong performance on NLU tasks through pretraining on billions of words. But what exact knowledge or skills do Transformer LMs learn from large-scale pretraining that they cannot learn from less data? We adopt four probing methods---classifier probing, information-theoretic probing, unsupervised relative acceptability judgment, and fine-tuning on NLU tasks---and draw learning curves that track the growth of these different measures of linguistic ability with respect to pretraining data volume using the MiniBERTas, a group of RoBERTa models pretrained on 1M, 10M, 100M and 1B words. We find that LMs require only about 10M or 100M words to learn representations that reliably encode most syntactic and semantic features we test. A much larger quantity of data is needed in order to acquire enough commonsense knowledge and other skills required to master typical downstream NLU tasks. The results suggest that, while the ability to encode linguistic features is almost certainly necessary for language understanding, it is likely that other forms of knowledge are the major drivers of recent improvements in language understanding among large pretrained models.