Reverse innovation commonly refers to an innovation initially launched in a developing country and later introduced to an advanced country. This study expands the definition of reverse innovation beyond its market-introduction focus by considering reversals in the flow of innovation in the ideation and product development phases. It then proposes a typology of global innovation with sixteen different types of innovation flows between advanced and emerging countries, ten of which are reverse innovation flows. The latter are further differentiated into weak and strong reverse innovation. This analytical framework allows recasting of current research at the intersection between innovation and international business. Of the ten reverse innovation flows, six are new and have not been covered in the literature to date. The study discusses merits and pitfalls of the model and formulates four research propositions for future investigation before concluding with implications for management and policy making.