Abstract Reduced-complexity models have considerable potential as tools for elucidating river behaviour over periods of 10 0 –10 4 years and, consequently, for addressing fundamental questions concerning the scale-dependent nature of explanation in geomorphology. This paper proposes a simple subdivision of reduced-complexity models of river behaviour into two categories that mirror methodological developments in fluvial geomorphology over the past 50 years. First, high-resolution cellular approaches that are implemented within a framework that resolves process-form feedbacks at small time and space scales. Second, models that incorporate section-averaged representations of channel geometry and processes, and that are typically underpinned by regime theory and equilibrium concepts. Examples of both model types are presented here, in the form of a cellular representation of stream braiding and a combined lattice-network model of alluvial fan evolution. Simulations conducted using these models demonstrate how small-scale process-form interactions determine the emergence of larger-scale channel and fan morphology and, in so doing, regulate system response to external forcing. In this sense, both models demonstrate that internal feedbacks play a critical role in controlling river responses to environmental change over historic and Holocene timescales. However, both classes of model are characterised by uncertainty in their parameterisation of geomorphic processes, such that internal feedbacks and thresholds for channel response to external forcing may vary substantially between competing models. Methods of refining both approaches are considered, and hybrid models based on lattice-network structures and mechanistic representations of channel process-form interactions are identified as a means of addressing the shortcomings of existing strategies.