The publication process both determines which research receives the most attention, and influences the supply of research through its impact on researchers' private incentives. We introduce a framework to study optimal publication decisions when researchers can choose (i) whether or how to conduct a study and (ii) whether or how to manipulate the research findings (e.g., via selective reporting or data manipulation). When manipulation is not possible, but research entails substantial private costs for the researchers, it may be optimal to incentivize cheaper research designs even if they are less accurate. When manipulation is possible, it is optimal to publish some manipulated results, as well as results that would have not received attention in the absence of manipulability. Even if it is possible to deter manipulation, such as by requiring pre-registered experiments instead of (potentially manipulable) observational studies, it is suboptimal to do so when experiments entail high research costs. We illustrate the implications of our model in an application to medical studies.