Correct simulation of stratospheric transport in Chemistry-Climate Models is a key requirement for their usefulness for future climate prediction. This study reports a comprehensive intercomparison of the simulation of the recent history of stratospheric transport in three generations of Chemistry-Climate Models, validating them against state-of-the-art observational datasets, clearly identifying major biases and discussing potential causes and impacts. The biases persist over model generations and, by some measures, increase for the most recent generation. These results have important implications for the climate science community, including model builders and those seeking to strengthen the underpinning science through process studies and new observations.