Arctic Amplification is a fundamental feature of past, present, and modelled future climate. However, the causes of this “amplification” within Earth’s climate system are not fully understood. To date, warming in the Arctic has been most pronounced in autumn and winter seasons, with this trend predicted to continue based on model projections of future climate. Nevertheless, the mechanisms by which this will take place are numerous, interconnected. and complex. Will future Arctic Amplification be primarily driven by local, within-Arctic processes, or will external forces play a greater role in contributing to changing climate in this region? Motivated by this uncertainty in future Arctic climate, this review seeks to evaluate several of the key atmospheric circulation processes important to the ongoing discussion of Arctic amplification, focusing primarily on processes in the troposphere. Both local and remote drivers of Arctic amplification are considered, with specific focus given to high-latitude atmospheric blocking, poleward moisture transport, and tropical-high latitude subseasonal teleconnections. Impacts of circulation variability and moisture transport on sea ice, ice sheet surface mass balance, snow cover, and other surface cryospheric variables are reviewed and discussed. The future evolution of Arctic amplification is discussed in terms of projected future trends in atmospheric blocking and moisture transport and their coupling with the cryosphere. As high-latitude atmospheric circulation is strongly influenced by lower-latitude processes, the future state of tropical-to-Arctic teleconnections is also considered.