Software developers are key players in the security ecosystem as they produce code that runs on millions of devices. Yet we continue to see insecure code being developed and deployed on a regular basis despite the existence of support infrastructures, tools, and research into common errors. This work provides a systematised overview of the relatively new field of Developer-Centred Security which aims to understand the context in which developers produce security-relevant code as well as provide tools and processes that that better support both developers and secure code production. We report here on a systematic literature review of 49 publications on security studies with software developer participants. We provide an overview of both the types of methodologies currently being used as well as the current research in the area. Finally, we also provide recommendations for future work in Developer-Centred Security.