The impacts of the global economic crisis of 2008, the intractable problems of persistent poverty and environmental change have focused attention on organizations that combine enterprise with an embedded social purpose. Scholarly interest in social enterprise (SE) has progressed beyond the early focus on definitions and context to investigate their management and performance. From a review of the SE literature, the authors identify hybridity, the pursuit of the dual mission of financial sustainability and social purpose, as the defining characteristic of SEs. They assess the impact of hybridity on the management of the SE mission, financial resource acquisition and human resource mobilization, and present a framework for understanding the tensions and trade‐offs resulting from hybridity. By examining the influence of dual mission and conflicting institutional logics on SE management the authors suggest future research directions for theory development for SE and hybrid organizations more generally.