The only way to obtain reliable empirical information on the intensity and topology of the weak magnetic fields of the quiet solar chromosphere is via the measurement and rigorous physical interpretation of polarization signals in chromospheric spectral lines. The observed Stokes profiles reported here are due to the Hanle and Zeeman effects operating in a weakly magnetized plasma that is in a state far from local thermodynamic equilibrium. The physical origin of their enigmatic linear polarization Q and U components is the existence of atomic polarization in their metastable lower-levels, which permits the action of a dichroism mechanism that has nothing to do with the transverse Zeeman effect. It is also pointed out that the population imbalances and coherences among the Zeeman sublevels of such long-lived atomic levels can survive in the presence of horizontal magnetic fields having intensities in the gauss range, and produce significant polarization signals. Finally, it is shown how the most recent developments in the observation and theoretical modelling of weak polarization signals are facilitating fundamental new advances in our ability to investigate the magnetism of the outer solar atmosphere via spectropolarimetry.