We describe and apply a method for estimating uplift rate histories from longitudinal river profiles. Our strategy is divided into three parts. First, we develop a forward model, which calculates river profiles from uplift rate histories. Height variation along a river profile is controlled by uplift rate and moderated by the erosional process. We assume that the erosional process can be represented by a combination of advection and diffusion, which are parameterized using four erosional constants. Second, we have posed and solved the geologically more interesting inverse problem: which uplift rate history minimizes the misfit between calculated and observed river profiles? The inverse algorithm has been tested on synthetic river profiles, which demonstrates that uplift rate histories can be reliably retrieved. Our tests show that the erosional process is dominated by advection (i.e., knickpoint retreat) and that changes in lithology and discharge play a secondary role in determining the transient form of a river profile. Finally, we have inverted river profiles from a series of African topographic swells, namely the Bié, South African, Namibian, Hoggar, and Tibesti domes. Fits between calculated and observed river profiles are excellent. Calculated uplift rate histories suggest that these domes grew rapidly during the last 30–40 million years. Uplift rate histories vary significantly from dome to dome but cumulative uplift histories agree closely with independent geologic estimates.