Engagement is widely recognized by higher education institutions, nation-states, and international organizations as the third pillar in the mission of university education. Despite the global reach of this concept, published research is disproportionately based on examples from the United States. This article brings to light the rich and extensive literature on university engagement from Latin America that is largely accessible only in Spanish. Among advocates for engaged universities differences exist in terms of the rationales that justify it and the means used to accomplish it. The authors identify the historical roots and current applications of three models of university engagement-- market-oriented, social justice, and university social responsibility--and use case studies from Latin America to explore more deeply the potential of the third model. This is then used as the basis for developing a research agenda that would inform practices in both the Global North and Global South.