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Peer-review plays a critical role in the scientific writing and publication ecosystem. To assess the efficiency and efficacy of the reviewing process, one essential element is to understand and evaluate the reviews themselves. In this work, we study the content and structure of peer reviews under the argument mining framework, through automatically detecting (1) the argumentative propositions put forward by reviewers, and (2) their types (e.g., evaluating the work or making suggestions for improvement). We first collect 14.2K reviews from major machine learning and natural language processing venues. 400 reviews are annotated with 10,386 propositions and corresponding types of Evaluation, Request, Fact, Reference, or Quote. We then train state-of-the-art proposition segmentation and classification models on the data to evaluate their utilities and identify new challenges for this new domain, motivating future directions for argument mining. Further experiments show that proposition usage varies across venues in amount, type, and topic.