The magnetic field is the main driver of the activity in the solar upper atmosphere, but its measurement is notoriously difficult. In order to determine the magnetic field in the chromosphere, transition region, and corona, we need to measure and interpret the polarization signals that the scattering of anisotropic radiation and the Hanle and Zeeman effects introduce in the emitted spectral line radiation. A number of recent advances have activated the development of this research field. The quantum theory of the generation and transfer of polarized radiation allows us to explain the polarization signals observed in chromospheric and coronal lines and to make successful predictions in unexplored spectral regions. The development of diagnostic techniques for the solar upper atmosphere has served to improve our empirical knowledge of the magnetic field in a variety of plasma structures, as well as to pave the way for their application to the unprecedented data that the new generation of solar telescopes are expected to provide. However, further improvements are required. The CLASP suborbital experiments have opened a new diagnostic window, namely ultraviolet (UV) spectropolarimetry as a tool for probing the magnetism and geometry of the upper chromosphere and transition region. A space telescope equipped with a UV spectropolarimeter would lead to major advances in our empirical understanding of solar magnetism.