Health promotion addresses issues from the simple (with well-known cause/effect links) to the highly complex (webs and loops of cause/effect with unpredictable, emergent properties). Yet there is no conceptual framework within its theory base to help identify approaches appropriate to the level of complexity. The default approach favours reductionism--the assumption that reducing a system to its parts will inform whole system behaviour. Such an approach can yield useful knowledge, yet is inadequate where issues have multiple interacting causes, such as social determinants of health. To address complex issues, there is a need for a conceptual framework that helps choose action that is appropriate to context. This paper presents the Cynefin Framework, informed by complexity science--the study of Complex Adaptive Systems (CAS). It introduces key CAS concepts and reviews the emergence and implications of 'complex' approaches within health promotion. It explains the framework and its use with examples from contemporary practice, and sets it within the context of related bodies of health promotion theory. The Cynefin Framework, especially when used as a sense-making tool, can help practitioners understand the complexity of issues, identify appropriate strategies and avoid the pitfalls of applying reductionist approaches to complex situations. The urgency to address critical issues such as climate change and the social determinants of health calls for us to engage with complexity science. The Cynefin Framework helps practitioners make the shift, and enables those already engaged in complex approaches to communicate the value and meaning of their work in a system that privileges reductionist approaches.