Social innovation and entrepreneurship (SIE) has emerged as a well-recognised field of practice and research amidst the intensified societal focus on complex social and environmental problems. Universities, as critical producers of knowledge and talents, are increasingly expected to create academic offerings that nurture leaners’ capacities for positive social change. However, research on SIE educational processes remains scant and is scattered among various disciplines. There is a lack of understanding of the overall development of SIE education in universities. This scoping review fills this gap by providing an overview of what drives universities’ adoption of SIE education and the current SIE curricula. It integrates studies that describe various SIE courses, focusing on curricular content, pedagogical practice, and outcome assessment. The review (1) identifies the major educational aims underpinning universities’ SIE offerings, (2) develops an integrative framework that specifies four approaches to SIE education, (3) synthesises and illustrates SIE teaching and learning practices, and (4) outlines opportunities for future research. The framework differentiates between education ‘about’, ‘for’, ‘through’, and ‘embedded with’ SIE. These approaches differ in the way educators conceptualise SIE and the way students engage with societal problems. The review also points to substantial gaps in our understanding of how to assess the impact of SIE education and how to sustain these novel educational practices within the university. It provides a base for integrating and advancing knowledge across the largely disparate literature on SIE education and highlights avenues for future research that can unpack SIE educational processes.