The Atlantic Meridional Overturning Circulation (AMOC) has profound impacts on various climate phenomena. Using both observations and simulations from the Coupled Model Intercomparison Project Phase 3 and 5, here we show that most models underestimate the amplitude of low‐frequency AMOC variability. We further show that stronger low‐frequency AMOC variability leads to stronger linkages between the AMOC and key variables associated with the Atlantic multidecadal variability (AMV), and between the subpolar AMV signal and northern hemisphere surface air temperature. Low‐frequency extratropical northern hemisphere surface air temperature variability might increase with the amplitude of low‐frequency AMOC variability. Atlantic decadal predictability is much higher in models with stronger low‐frequency AMOC variability and much lower in models with weaker or without AMOC variability. Our results suggest that simulating realistic low‐frequency AMOC variability is very important, both for simulating realistic linkages between AMOC and AMV‐related variables and for achieving substantially higher Atlantic decadal predictability. Plain Language Summary Our results provide a new perspective for understanding the important role of the Atlantic Meridional Overturning Circulation in Atlantic multidecadal variability and associated impacts and predictability. Our results indicate that the linkages between the Atlantic Meridional Overturning Circulation and Atlantic multidecadal variability, as well as the associated climate impacts and Atlantic decadal predictability, could be substantially hampered in Coupled Model Intercomparison Project models due to their underestimation of the amplitude of low‐frequency Atlantic Meridional Overturning Circulation variability. Key Points Most models underestimate the amplitude of low‐frequency AMOC variability Given stronger low‐frequency AMOC variability, linkages between the AMOC and the AMV and associated impacts on northern hemisphere surface temperature are stronger Atlantic decadal predictability is much higher (lower) in models with stronger (weaker) low‐frequency AMOC variability