This paper reviews research on open innovation that considers how and why firms commercialize external sources of innovations. It examines both the "outside-in" and "coupled" modes of open innovation. From an analysis of prior research on how firms leverage external sources of innovation, it suggests a four-phase model in which a linear process - (1) obtaining, (2) integrating, and (3) commercializing external innovations - is combined with (4) interaction between the firm and its collaborators. This model is used to classify papers taken from the top 25 innovation journals, complemented by highly cited work beyond those journals. A review of 291 open innovation-related publications from these sources shows that the majority of these articles indeed address elements of this inbound open innovation process model. Specifically, it finds that researchers have front-loaded their examination of the leveraging process, with an emphasis on obtaining innovations from external sources. However, there is a relative dearth of research related to integrating and commercializing these innovations. Research on obtaining innovations includes searching, enabling, filtering, and acquiring - each category with its own specific set of mechanisms and conditions. Integrating innovations has been mostly studied from an absorptive capacity perspective, with less attention given to the impact of competencies and culture (including "not invented here"). Commercializing innovations puts the most emphasis on how external innovations create value rather than how firms capture value from those innovations. Finally, the interaction phase considers both feedback for the linear process and reciprocal innovation processes such as cocreation, network collaboration, and community innovation. This review and synthesis suggests several gaps in prior research. One is a tendency to ignore the importance of business models, despite their central role in distinguishing open innovation from earlier research on interorganizational collaboration in innovation. Another gap is a tendency in open innovation to use "innovation" in a way inconsistent with earlier definitions in innovation management. The paper concludes with recommendations for future research that include examining the end-to-end innovation commercialization process, and studying the moderators and limits of leveraging external sources of innovation.