This review describes observations of the polar magnetic fields, models for the cyclical formation and decay of these fields, and evidence of their great influence in the solar atmosphere. The polar field distribution dominates the global structure of the corona over most of the solar cycle, supplies the bulk of the interplanetary magnetic field via the polar coronal holes, and is believed to provide the seed for the creation of the activity cycle that follows. A broad observational knowledge and theoretical understanding of the polar fields is therefore an essential step towards a global view of solar and heliospheric magnetic fields. Analyses of both high-resolution and long-term synoptic observations of the polar fields are summarized. Models of global flux transport are reviewed, from the initial phenomenological and kinematic models of Babcock and Leighton to present-day attempts to produce time-dependent maps of the surface magnetic field and to explain polar field variations, including the weakness of the cycle 23 polar fields. The relevance of the polar fields to solar physics extends far beyond the surface layers from which the magnetic field measurements usually derive. As well as discussing the polar fields' role in the interior as seed fields for new solar cycles, the review follows their influence outward to the corona and heliosphere. The global coronal magnetic structure is determined by the surface magnetic flux distribution, and is dominated on large scales by the polar fields. We discuss the observed effects of the polar fields on the coronal hole structure, and the solar wind and ejections that travel through the atmosphere. The review concludes by identifying gaps in our knowledge, and by pointing out possible future sources of improved observational information and theoretical understanding of these fields.
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