Governments can play great roles in their countries, regions, and cities; facilitating or leading the resolution of festering problems and opening new pathways for progress. Examples are more numerous than one might imagine and raise an important question: How do governments get great? This paper identifies 10 cases of great governments to answer 4 dimensions of this question: What kinds of interventions or changes help governments achieve greatness? Who leads these interventions or changes, and how? When do the interventions occur, and why? How are these changes sustained and implemented to ensure they yield results? The paper suggests two sets of answers to these concerns, combining such into rival theories that could explain how governments get great: "Solution and leader driven change" (SLDC) and "Problem driven iterative adaptation" (PDIA). It proposes using these two theories in future research about how governments foster the kinds of achievements one could call great and argues this research should employ a version of Theory Guided Process Tracking (TGPT) called systematic process analysis.