In this paper we take up the call to consider research and innovation to address major contemporary societal challenges, and the need to design innovation policies that go beyond the traditional competitiveness model. We conduct a broad review of the literature to analyse the diversity of innovation models. Although the linear model of innovation remains dominant, we identify three alternative models: users’ innovation, distributed innovation, and social innovation. We show that the models of innovation are related to different moral economies, and we discuss their ability to deal with the directionality of innovation. We also show that the current ‘democratisation of innovation’ (strongly related to these alternative models) does not necessarily allow societal challenges to be addressed. This analysis leads us to point out two issues. First, the need to make more space for alternative models, and second the need to better understand processes of generalisation through which local innovation acquires the capacity to reach wider users.