This Report by Nicola Dandridge considers the different approaches taken by higher education institutions, students, academics and policymakers towards the relationship between teaching and research. It notes how frequently the concept of research-informed teaching is invoked, yet how obscurely it is implemented. The relationship appears to mean different things to different people -- and administrations of all political complexions seem unconvinced by its value. The paper explores the ways in which the relationship between teaching and research can add significant value and have a transformative impact on students. It also notes examples where there is in practice no obvious relationship between the two activities, and where from students' perspectives there does not need to be. This HEPI Report finishes by asking whether it matters that the relationship is contested and sometimes opaque, and concludes that it does matter, at least in some respects.