The complexity sciences are subject to increasing policy interest from governments and international organisations as a means for fostering both social innovation and social entrepreneurship. However, there remains little conceptual clarity in how theories, concepts and ideas can be used consistently and productively. This article reviews the application of the complexity sciences in social innovation and social entrepreneurship scholarship overall and considers its implications for both fields. We outline how social innovation and social entrepreneurship can be conceptualised as complex processes, set within complex environments, tackling complex goals, and present a suitably revised model of the social innovation lifecycle. Based on this review - and the articles contributed to this special issue of Social Enterprise Journal – we argue that a complexity-informed perspective can contribute to scholarship and practice in three ways: as a rhetorical device, as an analytical framework for empirical analysis, and as a basis for developing new tools and methods for social innovation and social entrepreneurship. In this way academics can play a crucial role in helping policymakers and practitioners interested in the complexity sciences walk a line between fatalism and overstatement.