In this literature review, we show that a decade of research on sustainability as business models has led to the production of no less than 26 literature reviews on the topic, and how these reviews, through a dominant gap filling approach, propose unclear conceptual boundaries with sustainable assumptions that are largely unchallenged. We then follow the recently proposed problematization review by Alvesson and Sandberg as an alternative methodology to systemize the literature through a deliberate, systematic and ambitious effort and, confront the existing business model literature on sustainability with alternative points of interpretation. We pinpoint a deliberate narrow selection of sustainable business model articles within the management literature to map out problematic issues about their underlying theoretical assumptions. Then, we locate articles within the wider realms of the business model and sustainability literature to problematize these identified dominant assumptions. Our findings demonstrate taken for granted suppositions and categorize these between in-house assumptions, paradigmatic assumptions, and ideology assumptions. Finally, we further critique these findings and set out a future research agenda with the aim to guide management scholarly conversations on rethinking sustainable business model research.