Measuring precisely the faint polarization of the Far-Infrared and sub-millimetre sky is the next observational challenge of modern astronomy. In particular, detection the B-mode polarization from the cosmic microwave background (CMB) shall reveal the inflationary periods in the very early universe. Such measurements will require very high sensitivity and very low instrumental systematic effects. As for measurements of the CMB intensity, sensitive measurements of the CMB polarization will be made difficult by the presence of foreground emission from our own Milky Way, which is stronger than the faint polarized cosmological signal. Such foreground emission will have to be understood very accurately and removed from cosmological measurements. This polarized emission is also interesting in itself, since it brings information relevant to star formation processes, about the orientation of the magnetic field in our Galaxy through the alignment of dust grains. I will first summarize our current knowledge in this field. I will then describe the PILOT balloon-borne experiment project, which is dedicated to measuring precisely the polarization of faint diffuse dust emission from our Galaxy in the Far-Infrared.