This article argues that innovation may constitute a useful perspective on the link between society and arts and humanities research. Innovation is here seen as "something new put into practical use", and there are two reasons why it can be relevant for humanities. First, there has been an expansion of what innovation refers to; it is now commonly used for non-economic change processes in public, private and non-profit organisations. Second, arts and humanities are not unique in their contribution to innovation: good teaching, research, dissemination and external relations are the central contributions for all university disciplines. But this does not mean that it is easy to promote innovation at universities in general and in arts and humanities in particular. Through examples from a historical case study at the University of Oslo, different tensions are analysed related to indicators, infrastructure, teaching versus research and quality. All these need to be handled in such a way as to avoid fruitless conflicts, misunderstandings and poorly designed policies and university strategies.