For decades, Software Process Improvement (SPI) programs have been implemented, inter alia, to improve quality and speed of software development. To set up, guide, and carry out SPI projects, and to measure SPI state, impact, and success, a multitude of different SPI approaches and considerable experience are available. SPI addresses many aspects ranging from individual developer skills to entire organizations. It comprises for instance the optimization of specific activities in the software lifecycle as well as the creation of organization awareness and project culture. In the course of conducting a systematic mapping study on the state-of-the-art in SPI from a general perspective, we observed Global Software Engineering (GSE) becoming a topic of interest in recent years. Therefore, in this paper, we provide a detailed investigation of those papers from the overall systematic mapping study that were classified as addressing SPI in the context of GSE. From the main study's result set, a set of 30 papers dealing with GSE was selected for an in-depth analysis using the systematic review instrument to study the contributions and to develop an initial picture of how GSE is considered from the perspective of SPI. Our findings show the analyzed papers delivering a substantial discussion of cultural models and how such models can be used to better address and align SPI programs with multi-national environments. Furthermore, experience is shared discussing how agile approaches can be implemented in companies working at the global scale. Finally, success factors and barriers are studied to help companies implementing SPI in a GSE context.