The linearly polarized spectrum of the Sun that is formed by coherent scattering processes is as richly structured as the ordinary intensity spectrum, but the spectral structures look completely different and have different physical origins. Exploration of this ``second solar spectrum'' became possible with the advent of highly sensitive imaging polarimeters. While the identification of the previously unfamiliar spectral structures has led to new insights in atomic and line formation physics, the second solar spectrum lends itself to the exploration of magnetic fields in parameter domains that have been inaccessible to the Zeeman effect, in particular to weak fields and spatially unresolved tangled fields. The previous paradigm that most of the magnetic flux in the solar photosphere is in the form of intermittent kG flux tubes with tiny filling factors has thereby been shattered. Instead the whole photospheric volume appears to be seething with intermediately strong fields, of order 100 G, of significance for the overall energy balance of the solar atmosphere. According to the new paradigm the field behaves like a fractal with a high degree of self-similarity, spanning about 8 orders of magnitude in scale size, with half of the scales being spatially resolved, while the other half is in the spatially unresolved domain.