Extreme floods have dramatically altered landscapes on Earth and Mars through bedrock erosion, sediment deposition, and canyon formation. The Channeled Scabland of the Columbia Plateau in eastern Washington, USA, is perhaps the most striking example of such a landscape, where outburst floods from an ice-dammed glacial Lake Missoula eroded immense canyons and transported large volumes of sediment during the late Pleistocene. Despite advances in numerical modeling and geochemical exposure dating methods, it has remained a challenge to untangle the complex interactions between floodwater, bedrock, and glacial ice to link the size of a flood with its impact on the landscape. When the landscape experiences erosion in response to multiple extreme floods, erosional and depositional features represent a discrete flood or phase of flooding, when topography and other initial conditions may have differed substantially from their modern configuration. This discrepancy limits the accuracy with which the hydraulics of prior catastrophic floods can be assessed using geologic evidence indicating the extent of flooding. An improved understanding of how extreme floods erode bedrock, and how to account for this erosion when interpreting the landforms left behind by extreme floods, is therefore necessary. In this dissertation, I re-evaluate discharges of extreme floods after accounting for the topographic change due to flood-induced erosion, and evaluate these discharges in the context of geologic evidence. I first compare the discharges necessary to inundate mapped high-water marks assuming various configurations of ice and bedrock representative of different phases of the formation of Grand Coulee, the largest canyon in the Channeled Scabland. I find that only 15–20% of the discharge that reaches the high-water marks in the present-day topography is needed to inundate the same high-water marks when the topography is reconstructed to a partially incised state, yet these smaller discharges produce sufficient shear stress to erode bedrock and permit canyon incision. I then extended the analysis to include three flood channels, applying a novel method that extrapolates the long profiles of hanging tributaries to reconstruct the pre-flood topography that floods first encountered and to quantify the degree of erosion for each channel. Similarly, I find that discharges 20–40% of those necessary to inundate high-water marks on the modern topography do so on the reconstructed topography. These smaller discharges could transport the volume of rock eroded from their respective canyons in approximately 7–18 floods, consistent with depositional evidence limited to high-energy floods. These floods constitute about 20% of the approximately 100 total floods from glacial Lake Missoula. Finally, I investigate the timing of floods through the major flood-modified pathways across the Columbia Plateau, using cosmogenic nuclide exposure dating, to determine the rate and timing of incision and place canyon formation in the context of the broader history of flooding in this landscape. I find that the two largest canyons in the Channeled Scabland eroded rapidly over the course of a single glaciation. Together, these results suggest that discharge estimates which rely on the modern topography of flood-carved canyons produce substantial overestimates. However, when the erosion produced by extreme floods is understood and accounted for, canyon geometry can reveal a wealth of information about the floods that carved them.