We describe remnants of large (10⁷-10¹⁰ m³) Late Pleistocene to Holocene rockslides and rock avalanches that block(ed) rivers and are preserved in the Himalayas, the Tien Shan, and the New Zealand Southern Alps despite rates of uplift and erosion of up to 10 mm year^{- 1}. These natural dams control fluvial response on 10¹-10⁴ year timescales by (a) storing and releasing sediment during forced alluviation and fluvial re-incision; (b) relocating river channels through diversion or seepage; (c) inhibiting river erosion into bedrock; (d) forming persistent long-profile knickpoints and knickslopes associated with steep high-energy (> 10³ W m^{- 2}) breach and epigenetic bypass gorges and fluvial hanging valleys; and (e) shaping valley-floor morphology. Sediments indicate that rockslide-dammed lakes may persist up to 10⁴ years, before being drained or infilled. Several short-lived (10⁰-10² year) historical rockslide dams in the Indian and Nepal Himalayas and the Southern Alps have had marked volumetric impacts on catchment sediment budgets shortly following failure. Therefore, we caution against the linear extrapolation of sediment delivery from prehistoric rockslide dams through time as a response variable. We find reach-scale changes to channel gradient to be prominent and persistent indicators of fluvial response to large rock-slope failures.