The icy bodies in orbit beyond Neptune and known as Trans-Neptunian objects (TNOs), or Kuiper Belt objects, are the most distant objects of the Solar System accessible to direct investigation from the ground. The study of these objects, containing the least processed material of the Solar System, can help in understanding the still-puzzling accretion/evolution processes that governed planetary formation in our Solar System as well as in other dusty star discs. An ESO large programme has been devoted to obtaining simultaneous high quality visible and near-infrared spectroscopy and photometry of about forty objects with various dynamical properties. A few selected objects have also been observed with polarimetry to define their surface characteristics better and with detailed photometry to determine their rotational properties. The results provide a unique insight into the physical and surface properties of these remote objects.