The study of economic systems, and their guidance towards sustainability, can be enhanced by understanding how natural systems use materials and energy at various levels of system organization, how these levels interrelate, and how interrelationships change. Towards this end, the paper introduces natural economics as an approach to understanding the dynamics of hierarchical systems. We define the concepts of natural economics to facilitate the description and assessment of system change, and present dynamic modeling as a method for empirical research and as a tool for management decision making. We illustrate with empirical applications the use of dynamic modeling at various levels of system organization. Empirical illustrations range from dynamic models of simple physical systems of material transport, energy degradation and self-organized criticality to models of complex industrial systems, such as US iron ore mining and steel production. The insights derived from the natural economics approach are used to draw conclusions for the study and management of economy-environment interactions.