A control simulation in present-day conditions with the NCAR Community Climate System Model version 3 (CCSM3), a major contributor to the Intergovernmental Panel on Climate Change (IPCC) 4th Assessment Report (AR4), shows two regimes of Atlantic meridional overturning circulation (AMOC) variability, with an abrupt transition between them. We will first focus on the differences and the rapid transition between the two regimes of AMOC variability, i.e. a period with very regular and strong decadal variability, and one with irregular and weak multi-decadal variability, in terms of the mechanisms and associated global climate impact. We will then establish whether there are also multiple regimes and rapid transitions in the AMOC variability of the newly developed CCSM4 climate model, the CMIP5 participating version, and investigate and compare their mechanisms. CCSM3 exhibits a pronounced decadal variability of the AMOC in the present-day control integrations as well as global warming integrations. Two distinct regimes of decadal AMOC variability are apparent in the 700-yr long CCSM3 control integration with T85 atmospheric resolution (CCSM3-T85): a strong 20-year periodicity is seen for 300 years before an abrupt transition to a red noise-like variability lasting for the last 250 years. In the former regime, the decadal signal is also seen in the atmosphere, while there seems to be much less climatic impact in the latter. Regime transitions have been found in many coupled climate models, but they have not been considered explicitly other than in simplified models. Such non-stationarity exists in nature (as for ENSO and NAO) and may critically influence the predictability of the system. Hence, understanding what controls them and developing a methodology to do so is important. The analysis will be based on advanced statistical methods and complemented by numerical model experiments to elucidate the findings from the statistical analysis. In addition, we propose to use linear inverse modeling to assess the predictability of the AMOC. When possible, the findings will be compared with statistical signatures derived from the observations and reanalyses, so that the reliability of the model simulations can be assessed.