This comprehensive review highlights the complementary relationship between simple and comprehensive models in addressing key topics that describe Earth's atmospheric circulation. The systematic representation of models in hierarchies connects understanding from idealized systems to comprehensive models. This approach provides a straightforward way to understand and predict the real atmosphere. Three interconnected principles are introduced to characterize model hierarchies of the atmosphere. The rich diversity within the governing equations in the dynamical hierarchy is explored. The ability to isolate and understand atmospheric processes in the process hierarchy is described. Also highlighted is the importance of the physical domain and resolution in the hierarchy of scale. The discussion centers on the large scale circulation of the atmosphere and its interaction with clouds and convection, focusing on areas where simple models have had a significant impact. Our confidence in climate model projections of the future is based on our efforts to ground the climate predictions in fundamental physical understanding. This understanding is, in part, possible due to the hierarchies of idealized models that afford the simplicity required for understanding complex systems.