English: The quiet Sun is the region of the solar surface outside of sunspots, pores, and plages. In continuum intensity it appears dominated by granular convection. However, in polarized light the quiet Sun exhibits impressive magnetic activity on a broad range of scales, from the 30,000 km of supergranular cells down to the smallest magnetic features of about 100 km resolvable with current instruments. Quiet Sun fields are observed to evolve in a coherent way, interacting with each other as they are advected by the horizontal photospheric flows. They appear and disappear over surprisingly short time scales, bringing large amounts of magnetic flux to the solar surface. For this reason they may be important contributors to the heating of the chromosphere. Peering into such fields is difficult because of the weak signals they produce, which are easily affected, and even completely hidden, by photon noise. Thus, their evolution and nature remain largely unknown. In recent years the situation has improved thanks to the advent of high-resolution, high-sensitivity spectropolarimetric measurements and the application of state-of-the-art Zeeman and Hanle effect diagnostics. Here we review this important aspect of solar magnetism, paying special attention to the techniques used to observe and characterize the fields, their evolution on the solar surface, and their physical properties as revealed by the most recent analyses. We identify the main open questions that need to be addressed in the future and offer some ideas on how to solve them.