Extreme weather events across the world cause large variations in daily seasonal temperature and precipitation, potentially reducing grain yield and negatively affecting global food security. Thus, it is important to assess if crop growth models can simulate the yield losses caused by these extreme weather events. We tested if the DSSAT-NWheat crop simulation model, which has been successfully validated with many controlled field-experimental data across the world, can reproduce historical extreme low-yielding years at three global locations in the USA, France, and Australia. The crop model reproduced extreme low yields in some of the driest and hottest years at all three locations. However, the model failed to simulate some of the observed extreme low-yielding years. Also, the model simulated extreme low yields in some years that were not extreme low yielding in the observed records. Surprisingly, some of the driest and hottest years did not show up as observed extreme low-yielding years in the district records. This discrepancy could be explained by reporting yields, or in this case “not reporting extreme low yields” in district records, as indicated by large drops in harvested areas in extreme dry and hot seasons. Other discrepancies exist because crop models do not often consider many factors under farmer-field conditions that lead to extreme low yields in district records, including frost, hail and lodging, pests and diseases, and excess water. Historical district yield records are also limited for model testing due to unknown and changing aggregation across a district, possible omission of extreme low-yielding fields in some years, and unknown spatial and temporal varying cultivars and crop management, particularly in initial soil water conditions. In conclusion, we do not recommend using historical district yield records for model testing of extreme low yields.