Both the atmospheric and land surface conditions affect the dust cycle in the climate system. In particular, the occurrence of drought can modulate the emission of dust on interannual time scales. Studies have shown, however, that models generally do not represent dust variability, and that there is a large intermodel spread in the simulation of dust. In this study, we compare the relationship between drought and dust in 19 Global Circulation Models participating in Phase Six of the Coupled Model Intercomparison Project for historical (1950–2014) and future (2050–2100: SSP585) scenarios and MERRA‐2 reanalysis. The relationships between drought and dust (dust sensitivity to drought) are based on linear regression analysis. Our results show that MERRA‐2 reanalysis highly underestimates models' average dust emission. The Standardized Soil Moisture Index better explains the dust variability over most regions than the Standardized Precipitation Index, highlighting the importance of the condition of the land surface. Across models, the strength of the dust‐drought relationship explains much of the spread in interannual variability of dust emission over Southern Africa, Sahel, India, Australia, and North America, indicating models that capture this relationship generate greater variability. We also find that the correlation between models' dust‐drought relationship and mean emission is generally weaker compared to that with dust variability. In future scenarios, the intermodel spread in the projected changes in the dust variability is correlated to the intermodel spread in the projected changes in the models' dust sensitivity to drought in Australia, India, Middle East, South America, and Southern Africa.