Agile software development (ASD) methodologies can deliver various benefits but may also provide issues for software development projects. While research has identified numerous benefits and issues, it remains unclear how ASD’s core characteristics contribute to the different outcomes. Additionally, little attention has been paid to the project context factors that shape these outcomes. Building on the ASD core concepts framework by Baham and Hirschheim (2022) and 12 contextual factors, we conduct a qualitative systematic literature review of 122 studies to examine relationships between ASD core concepts, contextual characteristics, and the different outcomes (benefits and issues) of ASD. The implementation of core concepts like communication represents cornerstones for desirable benefits, while an inadequate realization of core concepts such as customer involvement can imply various issues. In addition, balancing their execution seems essential, as the highly-paced iterative nature of development and frequent inspections can imply negative consequences, besides their intended beneficial outcomes. Furthermore, we show that certain context factors, including high staff turnover, legacy systems, and volatile requirements can be problematic for ASD projects. Based on these insights, we develop a reconceptualized version of an agile sweet spot to determine an ideal setting for ASD projects. For academia, our work strengthens the theoretical core framework by identifying relationships among the core concepts and outcomes, while a research agenda guides future investigations into how ASD delivers its outcomes. Concerning practical implications, the findings can enable practitioners to improve the application of ASD by highlighting aspects that require dedicated attention to avoid issues.