We discuss the factors influencing the relationship between government policy-makers and scientists and how they affect the use of science in policy. We highlight issues related to context, values, culture, timeframes, communication and interpersonal relationships, providing insights from policy-makers and scientists. A spectrum of working strategies is given with examples of practical mechanisms that improve the effective use of science in policy. The shared governance model is a relatively mature approach with the potential to overcome many of the barriers discussed. At its core, shared governance, or co-production, invites policy-makers and scientists to develop and manage research priorities collaboratively. We explore the primary features of a successful shared governance arrangement, exemplified by the collaborative working model between the Australian Government Department of Agriculture and the Centre of Excellence for Biosecurity Risk Analysis. We conclude by outlining the advantages and disadvantages of the co-production of research priorities by scientists and policy-makers and present the learnings from its implementation in the biosecurity sector in Australia.