Efforts to diagnose the risks of a changing climate often rely on downscaled and bias-corrected climate information, making it important to understand the uncertainties and potential biases of this approach. Here, we perform a variance decomposition to partition uncertainty in global climate projections and quantify the relative importance of downscaling and bias-correction. We analyze simple climate metrics such as annual temperature and precipitation averages, as well as several indices of climate extremes. We find that downscaling and bias-correction often contribute substantial uncertainty to local decision-relevant climate outcomes, though our results are strongly heterogeneous across space, time, and climate metrics. Our results can provide guidance to impact modelers and decision-makers regarding the uncertainties associated with downscaling and bias-correction when performing local-scale analyses, as neglecting to account for these uncertainties may risk overconfidence relative to the full range of possible climate futures.