In this paper, I first explore the actors, events, evidence and arguments that enabled noncommunicable diseases (NCDs) to be constructed, from the 1990s onwards, as a ‘global epidemic’ and ‘global crisis’ that threatened social and economic development. I then examine how two decades of action since the Global Strategy on the Prevention and Control of Noncommunicable Diseases (World Health Organization 2000) has revealed the limits to that problematisation. In so doing, I actively trace the purposeful and inadvertent interplays between simplicity and complexity that have characterised the path of the NCD agenda since the early 1990s. As I argue, ‘clean problems’ may be deeply oxymoronic, but they are also a way of parsing complexity and simplicity and for key actors to explain why other disease constituencies have been relatively more successful in attracting global health funding. To support these arguments, I draw on interviews with forty key actors from the global ‘NCD community’ identified as playing an essential role in working towards the achievement of the first United Nations High Level Meeting in 2011. In critically exploring the oscillations of complexity and simplicity that characterise three decades of NCD advocacy, this paper brings analytical depth and qualitative rigour to a fascinating period of contemporary public health history.