Atlantic multidecadal variability (AMV) is the term used to describe the pattern of variability in North Atlantic sea surface temperatures (SSTs) that is characterized by decades of basinwide warm or cool anomalies, relative to the global mean. AMV has been associated with numerous climate impacts in many regions of the world including decadal variations in temperature and rainfall patterns, hurricane activity, and sea level changes. Given its importance, understanding the physical processes that drive AMV and the extent to which its evolution is predictable is a key challenge in climate science. A leading hypothesis is that natural variations in ocean circulation control changes in ocean heat content and consequently AMV phases. However, this view has been challenged recently by claims that changing natural and anthropogenic radiative forcings are critical drivers of AMV. Others have argued that changes in ocean circulation are not required. Here, we review the leading hypotheses and mechanisms for AMV and discuss the key debates. In particular, we highlight the need for a holistic understanding of AMV. This perspective is a key motivation for a major new U.K. research program: the North Atlantic Climate System Integrated Study (ACSIS), which brings together seven of the United Kingdom’s leading environmental research institutes to enable a broad spectrum approach to the challenges of AMV. ACSIS will deliver the first fully integrated assessment of recent decadal changes in the North Atlantic, will investigate the attribution of these changes to their proximal and ultimate causes, and will assess the potential to predict future changes.