The last few years have witnessed the emergence of hybrid business models, in particular, social enterprises, which combine social and economic concerns in the same extent. Social enterprises are ambidextrous organizations that conduct activities to meet the social needs of their target beneficiaries simultaneously with income generating activities. This hybrid operational nature raises new questions about the definition and identification of an effective operations management strategy. The present chapter aims to identify the main operational challenges faced by hybrid organization in order to open avenues for future research. Drawing on current literature, the main concepts, the definition of an operations strategy and the social enterprises as hybrid organizations, are discussed. Findings suggest that the main operational challenges arise from hybridity. This chapter contributes to the theory and practices of social enterprises and concludes by identifying some opportunities for future research.