During the last decade, many researchers have claimed that we are in the era of open innovation (OI). However, an extensive picture of the actual implementation of open innovation is still lacking. In order to address this gap, a research project was launched, called Open Innovation Survey, involving four European countries (Italy, UK, Sweden and Finland). The research project is focused on inbound innovation and it is aimed at identifying the OI models through which firms open their innovation funnel to their external partners, by means of an extended survey. The paper presents the first tentative results drawn from the survey, in terms of descriptive statistics (cluster analysis) and regressions, which allow depicting the different OI models actually adopted in the practice of companies. By relying on the conception of collaboration depth with two typical types of partners (scientific and business ones), four OI models are identified (open network innovators, supply chain collaborators, technology seekers and closed collaborators). Moreover, some determinants of such partner choices are outlined, as factors external and internal to the firms: technological trends are crucial to push firms towards external collaborations, above all with scientific partners; an aggressive innovation strategy, but also goals of innovation process efficiency exert a role. Lastly, the relationships among different OI models and both sides of innovation performance (novelty and efficiency) are investigated. In this regard, the organizational-managerial and social context factors emerge as relevant mediating variables, leading to a strong managerial implication: without an appropriate context, OI is not profitable.