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Understanding and predicting climate change have recently acquired a sense of urgency with the advent of serious climate-related food shortages and with the realization that human activities may have an influence on climate. Unfortunately, there is no comprehensive theory of climate to explain its variability, nor are there physical models that can adequately simulate the climate system. Hence there is a serious need for the development of quantitative mathematical models of climate, first to derive better understanding and ultimately to allow some degree of predictive capability. Many modeling approaches are available, ranging from simple one-dimensional representation of the vertical radiative processes in the atmosphere up to very complex mathematical systems that describe the three-dimensional behavior of the circulation of the atmosphere and ocean along with the chemical and thermodynamical processes that control the hydrological cycle and the existence of sea ice. Since the simpler models isolate the important physical processes that determine the climate, we weigh our discussion more heavily toward these but also discuss many aspects of the more complex models. We try to stress the fundamental physical basis of each kind of model and its contribution to the understanding of the simultaneous interactions (or feedbacks) of the many coupled processes that determine the climate. One difficulty in predicting climate change is the large degree of cancellation that occurs between many of the climatic feedback mechanisms. Considerable discussion is included of the applications of theories of baroclinic disturbances to the parameterization of eddy heat fluxes. Also stressed are basic energy balance approaches to the calculation of the surface temperature. Finally, we give our view of the future of climate modeling and argue that a flexible plan that vigorously pursues many avenues of approach is preferable. Although this review is often critical, we hope that it serves (1) to illustrate the multidisciplinary nature of climate simulation modeling and (2) to clarify the relative importance of individual contributions to the broader problems of understanding and (ultimately) predicting climate change.