The empirical investigation of the magnetic field in the outer solar atmosphere is a very important challenge in astrophysics. To this end, we need to identify, measure and interpret observable quantities sensitive to the magnetism of the upper chromosphere, transition region and corona. This paper provides an overview of the physics and diagnostic potential of spectropolarimetry in permitted spectral lines of the ultraviolet solar spectrum, such as the Mg ii h and k lines around 2800 Å, the hydrogen Lyman-α line at 1216 Å, and the Lyman-α line of He ii at 304 Å. The outer solar atmosphere is an optically pumped vapor and the linear polarization of such spectral lines is dominated by the atomic level polarization produced by the absorption and scattering of anisotropic radiation. Its modification by the action of the Hanle and Zeeman effects in the inhomogeneous and dynamic solar atmosphere needs to be carefully understood because it encodes the magnetic field information. The circular polarization induced by the Zeeman effect in some ultraviolet lines (e.g., Mg ii h & k) is also of diagnostic interest, especially for probing the outer solar atmosphere in plages and more active regions. The few (pioneering) observational attempts carried out so far to measure the ultraviolet spectral line polarization produced by optically pumped atoms in the upper chromosphere, transition region and corona are also discussed. We emphasize that ultraviolet spectropolarimetry is a key gateway to the outer atmosphere of the Sun and of other stars.