Reverse innovation commonly refers to an innovation initially launched in a developing country and later introduced to an advanced country. Adopting a linear innovation model with the four sequential phases of concept ideation, product development, primary target market introduction, and subsequent secondary market introduction, this study expands the espoused definition of reverse innovation beyond its market‐introduction focus with reversals in the flow of innovation in the ideation and product development phases. Recognizing that each phase can take place in different geographical locations, the paper then introduces a typology of global innovation with 16 different types of innovation flows between advanced and emerging countries, 10 of which are reverse innovation flows. The latter are further differentiated into weak and strong reverse innovation, depending on the number of innovation phases taking place in an emerging country. This analytical framework allows recasting of current research at the intersection between innovation and international business. Of the 10 reverse innovation flows, six are new and have not been covered in the literature to date. The study addresses questions of ethnocentrism and the continuity of the flow of innovation, and discusses possible extensions of the model with respect to the number of geographical categories and phases of innovation. Four research propositions highlight areas for future investigation, especially in the context of optimizing a firm's portfolio of global innovation competence and capability. The implications for management are concerned with internal and external resistance to reverse innovation. Most significantly, while greater recognition and power of innovation in formerly subordinate organizational units is inconvenient to some, the ability to leverage the potential of reverse innovation makes a firm more likely to succeed in global innovation overal