The need for policy makers to understand science and for scientists to understand policy processes is widely recognised. However, the science-policy relationship is sometimes difficult and occasionally dysfunctional; it is also increasingly visible, because it must deal with contentious issues, or itself becomes a matter of public controversy, or both. We suggest that identifying key unanswered questions on the relationship between science and policy will catalyse and focus research in this field. To identify these questions, a collaborative procedure was employed with 52 participants selected to cover a wide range of experience in both science and policy, including people from government, non-governmental organisations, academia and industry. These participants consulted with colleagues and submitted 239 questions. An initial round of voting was followed by a workshop in which 40 of the most important questions were identified by further discussion and voting. The resulting list includes questions about the effectiveness of science-based decision-making structures; the nature and legitimacy of expertise; the consequences of changes such as increasing transparency; choices among different sources of evidence; the implications of new means of characterising and representing uncertainties; and ways in which policy and political processes affect what counts as authoritative evidence. We expect this exercise to identify important theoretical questions and to help improve the mutual understanding and effectiveness of those working at the interface of science and policy.