The relationship between research and teaching has become a highly contested issue perhaps because evidence of synergy between them is modest and inconclusive. It could be argued that the separation of research and teaching is itself the result of policy and operational decisions made over some time to distinguish the way these activities are funded, managed, assessed and rewarded. Even if this were proven to be the case, however, this would not necessarily excuse higher education institutions (HEIs) from an obligation to maximise the beneficial relations between the two. This article explores whether institutions should attempt to do this and, for those that do, how this might be possible for institutional leaders and managers. It considers why the research-teaching link is problematic, the factors affecting whether positive links can be fostered and the implications for management and leadership in institutions and in academic departments. It argues that research, teaching and the relations between them are matters for strategic choices about the nature and future of an HEI and, ultimately, that views and actions on these matters reflect differing beliefs about the nature and purposes of Higher Education.