In post-publication peer review, scientific contributions are first published in open-access forums, such as arXiv or other digital libraries, and are subsequently reviewed and possibly ranked and/or evaluated. Compared to the classical process of scientific publishing, in which review precedes publication, post-publication peer review leads to faster dissemination of ideas, and publicly-available reviews. The chief concern in post-publication reviewing consists in eliciting high-quality, insightful reviews from participants. We describe the mathematical foundations and structure of TrueReview, an open-source tool we propose to build in support of post-publication review. In TrueReview, the motivation to review is provided via an incentive system that promotes reviews and evaluations that are both truthful (they turn out to be correct in the long run) and informative (they provide significant new information). TrueReview organizes papers in venues, allowing different scientific communities to set their own submission and review policies. These venues can be manually set-up, or they can correspond to categories in well-known repositories such as arXiv. The review incentives can be used to form a reviewer ranking that can be prominently displayed alongside papers in the various disciplines, thus offering a concrete benefit to reviewers. The paper evaluations, in turn, reward the authors of the most significant papers, both via an explicit paper ranking, and via increased visibility in search.