Programmers' mental models represent their knowledge and understanding of programs, programming concepts, and programming in general. They guide programmers' work and influence their task performance. Understanding mental models is important for designing work systems and practices that support programmers. Although the importance of programmers' mental models is widely acknowledged, research on mental models has decreased over the years. The results are scattered and do not take into account recent developments in software engineering. We analyze the state of research into programmers' mental models and provide an overview of existing research. We connect results on mental models from different strands of research to form a more unified knowledge base on the topic. We conducted a systematic literature review on programmers' mental models. We analyzed literature addressing mental models in different contexts, including mental models of programs, programming tasks, and programming concepts. Using nine search engines, we found 3678 articles (excluding duplicates). 84 were selected for further analysis. Using the snowballing technique, we obtained a final result set containing 187 articles. We show that the literature shares a kernel of shared understanding of mental models. By collating and connecting results on mental models from different fields of research, we uncovered some well-researched aspects, which we argue are fundamental characteristics of programmers' mental models. This work provides a basis for future work on mental models. The research field on programmers' mental models still faces many challenges rising from a lack of a shared knowledge base and poorly defined constructs. We created a unified knowledge base on the topic. We also point to directions for future studies. In particular, we call for studies that examine programmers working with modern practices and tools.