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The notion that the Atlantic Meridional Overturning Circulation (AMOC) can have more than one stable equilibrium emerged in the 1980s as a powerful hypothesis to explain rapid climate variability during the Pleistocene. Ever since, the idea that a temporary perturbation of the AMOC—or a permanent change in its forcing—could trigger an irreversible collapse has remained a reason for concern. Here we review literature on the equilibrium stability of the AMOC and present a synthesis that puts our understanding of past and future AMOC behavior in a unifying framework. This framework is based on concepts from Dynamical Systems Theory, which has proven to be an important tool in interpreting a wide range of model behavior. We conclude that it cannot be ruled out that the AMOC in our current climate is in, or close to, a regime of multiple equilibria. But there is considerable uncertainty in the location of stability …