A few years before the Hinode space telescope was launched, an investigation based on the Hanle effect in atomic and molecular lines indicated that the bulk of the quiet solar photosphere is significantly magnetized, due to the ubiquitous presence of an unresolved magnetic field with an average strength , ~ 130 G. It was pointed out also that this ``hidden'' field must be much stronger in the intergranular regions of solar surface convection than in the granular regions, and it was suggested that this unresolved magnetic field could perhaps provide the clue for understanding how the outer solar atmosphere is energized. In fact, the ensuing magnetic energy density is so significant that the energy flux estimated using the typical value of 1 km/s for the convective velocity (thinking in rising magnetic loops) or the Alfvén speed (thinking in Alfvén waves generated by magnetic reconnection) turns out to be substantially larger than that required to balance the chromospheric energy losses. Here we present a brief review of the research that led to such conclusions, with emphasis on a new three-dimensional radiative transfer investigation aimed at determining the magnetization of the quiet Sun photosphere from the Hanle effect in the Sr I 4607 Å line and the Zeeman effect in Fe I lines.