This paper concludes a special feature of Sustainability Science that explores a broad range of social value theoretical traditions, such as religious studies, social psychology, indigenous knowledge, economics, sociology, and philosophy. We introduce a novel transdisciplinary conceptual framework that revolves around concepts of ‘lenses’ and ‘tensions’ to help navigate value diversity. First, we consider the notion of lenses: perspectives on value and valuation along diverse dimensions that describe what values focus on, how their sociality is envisioned, and what epistemic and procedural assumptions are made. We characterise fourteen of such dimensions. This provides a foundation for exploration of seven areas of tension, between: (1) the values of individuals vs collectives; (2) values as discrete and held vs embedded and constructed; (3) value as static or changeable; (4) valuation as descriptive vs normative and transformative; (5) social vs relational values; (6) different rationalities and their relation to value integration; (7) degrees of acknowledgment of the role of power in navigating value conflicts. In doing so, we embrace the ‘mess’ of diversity, yet also provide a framework to organise this mess and support and encourage active transdisciplinary collaboration. We identify key research areas where such collaborations can be harnessed for sustainability transformation. Here it is crucial to understand how certain social value lenses are privileged over others and build capacity in decision-making for understanding and drawing on multiple value, epistemic and procedural lenses.