The Atlantic meridional overturning circulation (AMOC) represents the zonally integrated stream function of meridional volume transport in the Atlantic Basin. The AMOC plays an important role in transporting heat meridionally in the climate system. Observations suggest a heat transport by the AMOC of 1.3 PW at 26°N—a latitude which is close to where the Atlantic northward heat transport is thought to reach its maximum. This shapes the climate of the North Atlantic region as we know it today. In recent years there has been significant progress both in our ability to observe the AMOC in nature and to simulate it in numerical models. Most previous modeling investigations of the AMOC and its impact on climate have relied on models with horizontal resolution that does not resolve ocean mesoscale eddies and the dynamics of the Gulf Stream/North Atlantic Current system. As a result of recent increases in computing power, models are now being run that are able to represent mesoscale ocean dynamics and the circulation features that rely on them. The aim of this review is to describe new insights into the AMOC provided by high‐resolution models. Furthermore, we will describe how high‐resolution model simulations can help resolve outstanding challenges in our understanding of the AMOC.