A number of drivers for contemporary research are focusing attention on how to achieve public engagement in research undertaken by Higher Education Institutes (HEIs). In 2008, RCUK funded six ‘Beacons for Public Engagement’. We sought to understand how each Beacon had created the conditions for two-way engagement in the research design and delivery. We undertook an initial scoping study of the organisational culture within each Beacon and, using maximum variation sampling, selected seven projects which were our case studies. The analysis of the findings from these case studies from a complex systems perspective led us to conceptualise an ‘engagement cycle' which has three phases or elements: creating the conditions; co-creation of research; and, feedback loops to inform ongoing and future research. In this chapter, we discuss the approach we used to gather the data, how complexity theory underpins the approach and the interpretation of the findings, and how the results led to the engagement cycle.