The need to visualise the complexity of the determinants of population health and their interactions inspired the development of the rainbow model. In this commentary we chronicle how variations of this model have emerged, including the initial models of Haglund and Svanström (1982), Dahlgren and Whitehead (1991), and the Östgöta model (2014), and we illustrate how these models have been influential in both public health and beyond. All these models have strong Nordic connections and are thus an important Nordic contribution to public health. Further, these models have underpinned and facilitated other examples of Nordic leadership in public health, including practical efforts to address health inequalities and design new health policy approaches. Apart from documenting the emergence of rainbow models and their wide range of contemporary uses, we examine a range of criticisms levelled at these models – including limitations in methodological development and in scope. We propose the time is ripe for an updated generic determinants of health model, one that elucidates and preserves the core value in older models, while recognising the developments that have occurred over the past decades in our understanding of the determinants of health. We conclude with an example of a generic model that fulfills the general purposes of a determinants of health model while maintaining the necessary scope for further adjustments to be made in the future, as well as adjustments to location or context-specific purposes, in education, research, health promotion and beyond.