Corporate Engagements with Startups (CEwS) are Open Innovation initiatives in which large established companies interact with startups aiming at improving innovation performance. Complementary characteristics of established companies (e.g. resource availability, inertia…) and startups (resource scarcity, flexibility, technologies…) are starting points for such engagements. However, large companies and startups are remarkably different so that working together can be overly challenging. Especially for large companies, many intricacies emerge to interact with nascent businesses (e.g. processes, culture, resource sharing, information disclosure, etc.). This study summarizes the current literature on CEwS and identifies the main strands and antecedents of this phenomenon, as well as the main reference models available in the literature. Then, the paper presents and discusses some open questions for innovation management under the perspective of large companies, based on the gaps identified between the presented literature on CEwS and the organizational debate within the innovation management field. Finally, we present implications for theory and practice and suggest directions for future studies on CEwS.