Anticipating the need for infrastructure in cislunar space to support telecommunications, navigation, and crew and cargo transportation, the available periodic orbits that encounter both the Earth and the moon, termed cyclers, should be characterized and their utility should be evaluated using appropriate metrics. Using the planar circular restricted three-body problem to model spacecraft motion in the Earth-moon system, a classification scheme based on resonant orbits and homoclinic connections is proposed to summarize two broad cycler classes. One class consists of high-energy near-elliptical cyclers; the second class consists of low-energy cyclers that use the dynamical structure associated with the collinear libration point between the Earth and moon. The first class is organized around resonant cyclers that can be easily characterized and are representative of the whole class. The second class of cyclers is organized by the homoclinic connections associated with the unstable Lyapunov family of periodic orbits around the libration point between the Earth and moon. The homoclinic connections bound sets of cyclers, provide close approximations ofthe cyclers, and can thus be used to identify their characteristics. Computational methods for both cycler classes, based on continuation and differential correction, are discussed and demonstrated. Copyright © 2010 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.