Safety cases have long been required by many safety standards and guidelines. Particularly in the UK, new systems in key sectors such as defence, nuclear and rail need a safety case before they can be certified and approved. Proponents of safety cases have justified this on the basis of some explicit theory (e.g. that of Toulmin) and by using a variety of plausible, common-sense arguments. There has, unsurprisingly, been a large amount of research on safety cases, on how to structure them, how to review them, and (increasingly) how to formalise them mathematically or generate them automatically. However, there has been very little research that evaluates safety case methods and practices as a whole. Do they “work”, in terms of safety or other benefits? If so, when, how and why do they work? In particular, there has been almost no research on “the science of the safety case” — no systematic marshalling of all the claims used to promote safety case methods, and importantly no research programme to test each one. In this paper, we identify the key claims made by safety case proponents. We emphasise claims about mechanism — those about how and why safety cases provide benefits. From there, we spell out how to identify the most important research questions raised by those claims and outline a community-wide research approach that could help answer those questions. To do this will require that we first understand how people currently develop safety cases and what their concerns, needs, constraints and problems are. There is little point in testing hypotheses and solutions that do not target real problems.