National governments spend significant amounts of money supporting public research. However, in an era where the international economic climate has led to budget cuts, policymakers increasingly are looking to justify the returns from public investments, including in science and innovation. The so-called 'impact agenda' which has emerged in many countries around the world is part of this response; an attempt to understand and articulate for the public what benefits arise from the research that is funded. The United Kingdom is the most progressed in implementing this agenda and in 2014 the national research assessment exercise, the Research Excellence Framework, for the first time included the assessment of research impact as a component. For the first time within a dual funding system, funding would be awarded not only on the basis of the academic quality of research, but also on the wider impacts of that research. In this paper we outline the context and approach taken by the UK government, along with some of the core challenges that exist in implementing such an exercise. We then synthesise, together for the first time, the results of the only two national evaluations of the exercise and offer reflections for future exercises both in the UK and internationally.