Abstract Automatic summarization is typically treated as a 1-to-1 mapping from document to summary. Documents such as news articles, however, are structured and often cover multiple topics or aspects; and readers may be interested in only some of them. We tackle the task of aspect-based summarization, where, given a document and a target aspect, our models generate a summary centered around the aspect. We induce latent document structure jointly with an abstractive summarization objective, and train our models in a scalable synthetic setup. In addition to improvements in summarization over topic-agnostic baselines, we demonstrate the benefit of the learnt document structure: we show that our models (a) learn to accurately segment documents by aspect; (b) can leverage the structure to produce both abstractive and extractive aspectbased summaries; and (c) that structure is particularly advantageous for summarizing long documents. All results transfer from synthetic training documents to natural news articles from CNN/Daily Mail and RCV1