I will review the use of the intergalactic medium (IGM), diffuse matter between galaxies (the so-called cosmic web), as a cosmological observable. Due to its intrinsic nature, the IGM is highly complementary to other probes like the cosmic microwave background and galaxy clustering and allows to measure the matter perturbations down to small scales and at high redshift. In recent years, baryonic acoustic oscillations have been detected at high redshift and unprecedented tight constraints on dark matter nature and neutrino mass have also been obtained, using IGM data (mainly from low resolution BOSS and high resolution quasar spectra from HIRES/Keck). The IGM is thus a tracer of our Universe medium/small scale structure over a significant portion of cosmic history. The IGM can be used to address fundamental physical questions like the nature of dark matter, neutrino masses, possible extension of the standard cosmological model, and offers important clues on the cosmic cycle of baryons and the galaxy/IGM interplay.