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Polar front jet stream variability is responsible for instances of extreme weather and is crucial for regional climate change. The North Atlantic Polar Front jet stream is of particular significance to the heavily populated areas of western Europe and eastern North America as storm track variability, atmospheric modes of variability such as the North Atlantic Oscillation (NAO), temperature and rainfall are all intimately linked with jet stream changes. Although seasonal and interannual variability are often attributed to internal variability, there are several possible drivers of polar front jet stream changes that are reviewed in this study. Cryospheric effects from sea-ice extent and snow cover, oceanic effects from North Atlantic sea-surface temperatures and tropical influences such as the El-Niño Southern Oscillation, and stratospheric effects due to stratospheric circulation variability, solar variability, volcanic eruptions and the Quasi-Biennial Oscillation are all identified in the literature as factors that impact on the Atlantic Polar Front jet stream. These drivers of jet stream variability can oppose or reinforce one another, and there are some indications of possible nonlinear interactions between them. We also review the modelling of jet stream variability. While a consensus has now been reached that some observed drivers can be reproduced in climate models, we conclude that improved understanding of more recently identified drivers of the Atlantic extratropical jet stream is crucial for making progress in regional climate predictions on all timescales from months to decades ahead.