Efforts to diagnose the risks of a changing climate often rely on downscaled and bias-corrected climate information, making it important to quantify the uncertainties and potential biases of this approach. Here, we perform a variance decomposition to partition uncertainty in global projections of several metrics of climate change, including many indices of climate extremes. By leveraging 5 different downscaled and bias-corrected ensembles with parent models from the CMIP6 repository, we quantify the relative importance of scenario uncertainty, model uncertainty, downscaling and bias-correction uncertainty, and interannual variability. Our results are strongly heterogeneous across space, time, and climate metrics, but in general we find that downscaling and bias-correction drive a considerable fraction of projection spread and can often represent the primary source of uncertainty. We find that downscaling and bias-correction are particularly important sources of uncertainty in projections of precipitation and of climate extremes. Our results suggest that impact modelers and decision-makers who rely on a single set of downscaled and bias-corrected outputs may risk overconfidence relative to the full range of possible climate futures.