The Earth’s magnetosphere exhibits substantial complexity in many of its physical properties. Particle populations wax and wane and magnetic fields fluctuate on virtually all observed time scales, from less than 1 minute to many days. Much of the variability of the magnetosphere and its interaction with the ionosphere can be ascribed to the phenomena termed “substorms” and “storms.” Ample evidence is found that these geospace disturbances, though exhibiting event-to-event differences, are remarkably repetitive and have basic underlying similarities. The ring current development, radiation belt particle changes, and basic substorm patterns suggest a high degree of coherence in the phenomena. Observations, modeling, and basic physical properties are discussed here that point to a relatively ordered, low-dimensional underlying dynamics in the magnetosphere. These results suggest that nonlinear processes and couplings introduce much of the observed complexity in magnetospheric particle and field changes.