We examine how soil moisture variability and trends affect the simulation of temperature and precipitation extremes in six global climate models using the experimental protocol of the Global Land-Atmosphere Coupling Experiment of the Coupled Model Intercomparison Project, Phase 5 (GLACE-CMIP5). This protocol enables separate examinations of the influences of soil moisture variability and trends on the intensity, frequency, and duration of climate extremes by the end of the 21st century under a business-as-usual (Representative Concentration Pathway 8.5) emission scenario. Removing soil moisture variability significantly reduces temperature extremes over most continental surfaces, while wet precipitation extremes are enhanced in the tropics. Projected drying trends in soil moisture lead to increases in intensity, frequency, and duration of temperature extremes by the end of the 21st century. Wet precipitation extremes are decreased in the tropics with soil moisture trends in the simulations, while dry extremes are enhanced in some regions, in particular the Mediterranean and Australia. However, the ensemble results mask considerable differences in the soil moisture trends simulated by the six climate models. We find that the large differences between the models in soil moisture trends, which are related to an unknown combination of differences in atmospheric forcing (precipitation, net radiation), flux partitioning at the land surface, and how soil moisture is parameterized, imply considerable uncertainty in future changes in climate extremes.