When the polarimetric sensitivity and the angular resolution exceed a threshold, magnetic fields show up almost everywhere on the solar surface. Here I revise the observational properties of the weakest polarization signals, which appear in the InterNetwork (IN) regions. We already have some information on the magnetic field strengths and inclinations, mass motions, lifetimes, magnetic fluxes, magnetic energies, etc. Since the IN covers a substantial faction of the solar surface, it may account for most of the unsigned magnetic flux and energy existing on the solar surface at any given time. This fact makes IN fields potentially important to understand the global magnetic properties of the Sun (e.g. the structure of the quiet solar corona, an issue briefly addressed here). The spectropolarimeters on board of SolarB have the resolution and sensitivity to routinely detect these IN fields.