The stratospheric Brewer–Dobson circulation (BDC), responsible for transporting mass, tracers and heat globally in the stratosphere, is evaluated in a set of state-of-the-art climate models. The acceleration of the BDC in response to increasing greenhouse gases is most robust in the lower stratosphere. At higher levels, the well-known inconsistency between model and observational BDC trends can be partly reconciled by accounting for limited sampling and large uncertainties in the observations.