The era of digitization coincides with a growing interest in social and environmental sustainability. Management scholars, therefore, turned their attention to the intersection of both trends, seeking a better understanding of how firms can manage digital sustainability. Business models are a central element in the strategic management of digital sustainability. Due to the diverse roots in the digitization literature, the sustainability literature and the business model literature, previous work on digital-sustainable business models is highly fragmented. We, therefore, develop a strategic management framework and conduct an integrative literature review to synthesize fragmented insights, covering 134 studies published between 2007 and 2023 in leading academic journals. Examining the synthesized body of knowledge from the lens of affordances and our framework's inclusive strategic management perspective, we then identify promising avenues for further strategy research. Among others, future research should examine complementarities and conflicts between the three business model dimensions (value propositions, value creation and delivery processes, value capture mechanisms), between multiple options within each dimension, between different digital technologies, between various digital affordances, between digitalization and sustainability and between the outcomes of the triple-bottom-line. More efforts should also be directed towards the antecedents and boundary conditions of digital-sustainable business models and towards questions of generalizability, especially towards generalizable theoretical mechanisms. Our framework, synthesis and research agenda support strategy scholars in advancing our understanding of business models for digital sustainability.