Context: The proper management of people can help software organisations to achieve higher levels of success. However, the limited attention paid to the appropriate use of theories to underpin the research in this area leaves it unclear how to deal with human aspects of software engineers, such as motivation and satisfaction. Objectives: This article aims to expose what drives the motivation and satisfaction of software engineers at work. Methods: A multiple case study was conducted at four software organisations in Brazil. For 11 months, data was collected using semi-structured interviews, diary studies, and document analyses. Results: The Theory of Motivation and Satisfaction of Software Engineers (TMS-SE), presented in this article, combines elements from well established theories with new findings, and translates them into the software engineering context. Conclusion: The TMS-SE advances the understanding of people management in the software engineering field and presents a strong conceptual framework for future investigations in this area.