NLP is currently dominated by language models like RoBERTa which are pretrained 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? To explore this question, we adopt five styles of evaluation: classifier probing, information-theoretic probing, unsupervised relative acceptability judgments, unsupervised language model knowledge probing, and fine-tuning on NLU tasks. We then draw learning curves that track the growth of these different measures of model 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 these LMs require only about 10M to 100M words to learn to reliably encode most syntactic and semantic features we test. They need a much larger quantity of data 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, unidentified, forms of knowledge are the major drivers of recent improvements in language understanding among large pretrained models.