In order to better understand the evolution of rift‐related topography and sedimentation, we present the results of a numerical modelling study in which elevation changes generated by extensional fault propagation, interaction and linkage are used to drive a landscape evolution model. Drainage network development, landsliding and sediment accumulation in response to faulting are calculated using CASCADE, a numerical model developed by Braun and Sambridge, and the results are compared with field examples. We first show theoretically how the ‘fluvial length scale’, L _f, in the fluvial incision algorithm can be related to the erodibility of the substrate and can be varied to mimic a range of river behaviour between detachment‐limited (DL) and transport‐limited (TL) end‐member models for river incision. We also present new hydraulic geometry data from an extensional setting which show that channel width does not scale with drainage area where a channel incises through an area of active footwall uplift. We include this information in the coupled model, initially for a single value of L _f, and use it to demonstrate how fault interaction controls the location of the main drainage divide and thus the size of the footwall catchments that develop along an evolving basin‐bounding normal fault. We show how erosion by landsliding and fluvial incision varies as the footwall area grows and quantify the volume, source area, and timing of sediment input to the hanging‐wall basin through time. We also demonstrate how fault growth imposes a geometrical control on the scaling of river discharge with downstream distance within the footwall catchments, thus influencing the incision rate of rivers that drain into the hanging‐wall basin. Whether these rivers continue to flow into the basin after the basin‐bounding fault becomes fully linked strongly depends on the value of L _f. We show that such rivers are more likely to maintain their course if they are close to the TL end member (small L _f); as a river becomes progressively more under supplied, i.e. the DL end member (large L _f), it is more likely to be deflected or dammed by the growing fault. These model results are compared quantitatively with real drainage networks from mainland Greece, the Italian Apennines and eastern California. Finally, we infer the calibre of sediments entering the hanging‐wall basin by integrating measurements of erosion rate across the growing footwall with the variation in surface processes in space and time. Combining this information with the observed structural control of sediment entry points into individual hanging‐wall depocentres we develop a greater understanding of facies changes associated with the rift‐initiation to rift‐climax transition previously recognised in syn‐rift stratigraphy.