The Geophysical Fluid Dynamics Laboratory (GFDL) of the National Oceanic and Atmospheric Administration participates along with a number of model centers around the world in constructing state‐of‐the‐art climate models for use in studies for climate change and prediction. GFDL's latest multipurpose atmosphere‐ocean coupled climate model, CM4.0, is described here. It consists of GFDL's latest atmosphere and land models at about 100 km horizontal resolution and ocean and sea ice models at roughly 25 km horizontal resolution. A handful of standard experiments have been conducted with CM4.0 for participation in the Coupled Model Intercomparison Project Phase 6, an archive of climate model results utilized by the Intergovernmental Panel on Climate Change and the climate research community more generally. The model results have been extensively evaluated against observations. This paper makes the case that CM4.0 ranks high among state‐of‐the‐art coupled climate models by many measures of bias in the simulated climatology and in its ability to capture modes of climate variability such as the El Niño‐Southern Oscillation and Madden‐Julian Oscillation. The paper also discusses some potential weaknesses, including unrealistically large internal variability in the Southern Ocean and insufficient warming before 1990 in the simulation of the twentieth century.