Biases in climate model simulations introduce biases in subsequent impact simulations. Therefore, bias correction methods are operationally used to post-process regional climate projections. However, many problems have been identified, and some researchers question the very basis of the approach. Here we demonstrate that a typical cross-validation is unable to identify improper use of bias correction. Several examples show the limited ability of bias correction to correct and to downscale variability and demonstrate that bias correction can cause implausible climate change signals. Bias correction cannot overcome major model errors, and naive application might result in ill-informed adaptation decisions. We conclude with a list of recommendations and suggestions for future research to reduce, post-process and cope with climate model biases.