Atlantic multidecadal variability (AMV) has long been thought to be an expression of low-frequency variability in the Atlantic Meridional Overturning Circulation (AMOC). However, alternative hypotheses have been forwarded, including that AMV is primarily externally forced. Here, we review the current state of play by assessing historical simulations made for the sixth coupled model intercomparison project (CMIP6). Overall, the importance of external forcing is sensitive to the type of AMV index used, due to the importance of globally coherent externally forced signals in the models. There are also significant contrasts between the processes that drive internally and externally forced AMV, but these processes can be isolated by exploring the multivariate expression of AMV. Specifically, internal variability in CMIP6 models is consistent with an important role of ocean circulation and AMOC and the externally forced AMV is largely a surface-flux forced mechanism with little role for the ocean. Overall, the internal multivariate fingerprint of AMV is similar to the observed, but the externally forced fingerprint appears inconsistent with observations. Therefore, climate models still suggest a key role for ocean dynamics, and specifically AMOC, in observed AMV. Nevertheless, models remain deficient in a number of areas, and a stronger role for externally forced dynamical changes cannot be ruled out. This article is part of a discussion meeting issue ‘Atlantic overturning: new observations and challenges’.