The quasi‐biennial oscillation (QBO) of the zonal mean zonal wind is the primary mode of variability in the tropical lower stratosphere. The QBO is characterized by alternating easterly westerly shear layers that descend down from ∼10 to 100 hPa. The QBO is also seen in lower stratospheric tropical temperature, water vapor, and ozone and affects tropospheric variability through various teleconnections. We examine here the progress in simulating the QBO in the Coupled Model Intercomparison Project (CMIP) models, more specifically in CMIP3, CMIP5, and CMIP6 models. We show that the number of models that are able to simulate the QBO has increased from 0 in CMIP3, to 5 in CMIP5, to 15 in CMIP6. While the number of models with an internally generated QBO has tripled from CMIP5 to CMIP6, the fidelity of the simulation averaged over the CMIP models has not improved. We show that CMIP5 and CMIP6 models represent the QBO period and latitudinal extent quite well; however the QBO amplitude is shifted upwards relative to observations resulting in large underestimation of QBO amplitude at all levels below 20 hPa. The underestimation of QBO amplitude in the lowermost stratosphere and lack of variations downward to the tropopause and below will likely impact the quality of teleconnections seen in the current generation Earth system models.