That fluvial geomorphology has not produced more and better models for prediction is due to some severe difficulties inherent in the subject and to certain other impediments that are more psychological in nature. A major inherent difficulty is the strong nonlinearity of the dominant process, namely sediment transport by running water, which not only causes serious mathematical obstacles but also underlies an instability that in turn gives rise to a significant random element in fluvial systems. Another deep-seated difficulty is the extreme differences in characteristic time scales of the interacting processes, such as slope and channel processes. A serious psychological impediment is the commonly held notion that geomorphology should be derived entirely from supposedly more fundamental sciences, such as fluid mechanics. Even more serious is a pervasive disagreement among fluvial geomorphologists over legitimacy of aims, methods, and basics. This lack of paradigm shows signs of change, however, most significantly in the nascent realization that particular processes do not necessarily produce corresponding particular forms. The problem of process and form has two interdependent aspects: derivation of the fundamental differential equations governing landform evolution requires investigating processes in terms of form, that is, in terms of variables such as elevation and gradient; and solution of the equations requires studying landforms to identify relevant special characteristics, especially ones that may simplify the problem. Other propitious influences that will benefit geomorphological research are tight budgets, new research tools and techniques, and the necessity for a better scientific base to support environmental engineering and planetary geology. Finally, and most important, the accumulation of an imposing stockpile of poorly understood observations on fluvial systems and of a substantial fund of highly promising ideas about them makes fluvial geomorphology ripe for progress toward powerful new models for prediction.