This work reviews our understanding of the magnetic fields observed in the quiet Sun. The subject has undergone a major change during the last decade (quiet revolution), and it will remain changing since the techniques of diagnostic employed so far are known to be severely biased. Keeping these caveats in mind, our work covers the main observational properties of the quiet Sun magnetic fields: magnetic field strengths, unsigned magnetic flux densities, magnetic field inclinations, as well as the temporal evolution on short time-scales (loop emergence), and long time-scales (solar cycle). We also summarize the main theoretical ideas put forward to explain the origin of the quiet Sun magnetism. A final prospective section points out various areas of solar physics where the quiet Sun magnetism may have an important physical role to play (chromospheric and coronal structure, solar wind acceleration, and solar elemental abundances).
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