AbstractGeomorphology is currently in a period of resurgence as we seek to explain the diversity, origins and dynamics of terrain on the Earth and other planets in an era of increased environmental awareness. Yet there is a great deal we still do not know about the physics and chemistry of the processes that weaken rock and transport mass across a planet's surface. Discovering and refining the relevant geomorphic transport functions requires a combination of careful field measurements, lab experiments, and use of longer‐term natural experiments to test current theory and develop new understandings. Landscape evolution models have an important role to play in sharpening our thinking, guiding us toward the right observables, and mapping out the logical consequences of transport laws, both alone and in combination with other salient processes. Improved quantitative characterization of terrain and process, and an ever‐improving theory that describes the continual modification of topography by the many and varied processes that shape it, together with improved observation and qualitative and quantitative modelling of geology, vegetation and erosion processes, will provide insights into the mechanisms that control catchment form and function. This paper reviews landscape theory – in the form of numerical models of drainage basin evolution and the current knowledge gaps and future computing challenges that exist. Copyright © 2010 John Wiley & Sons, Ltd.