Agenda driven research, with topics defined by funding agencies, political actors or lobby groups, is constantly gaining in importance. At its core is the commitment to tackling pressing issues of our time, for example in the societal challenges calls of the Horizon2020 programme of the European Union. This focus on relevance and impact, however, is often seen as a threat to curiosity driven research, undermining or even delegitimising it. This contribution will argue that this is a false dichotomy and will explore the specific challenges and opportunities of the impact debate for the Humanities. After outlining some major problematic features of the impact concept for the Humanities it makes  recommendations how these might be addressed. It further illustrates its points with reference to selected examples of the UK’s 2014 Research Excellence Framework impact case studies.