Innovation research has grown steadily over the years, with different foci and methodological approaches. The abundance of literature on the topic makes clear that innovative processes are at the centre of many narratives, in academia, the public sector in general and in industry. This contribution scopes the literature and traces some key considerations regarding a determining factor: openness. The paper explores the literature in order to narrow down the characteristics of so-called ‘open innovation’. An emphasis is placed on the main channels that determine collaboration practices, particularly between academia and the private sector, namely university-industry linkages. It focuses on open transfers of knowledge and open science research practices. The overarching discussion develops key questions underlining the relevance of open innovation for science, industry and the consolidation of narratives promoting access and collaboration. The paper concludes by offering some insights into trends and challenges from a research perspective as well as from the view of innovation dynamics.