Since 2002, we started an observational program on Jupiter Trojans at ESO-NTT, ESO-VLT and TNG. We carried out visible and near-infrared spectroscopy and photometry of members of dynamical families, as defined by Beauge and Roig (2001), and of several background objects. The aim of these observations was to improve our knowledge of the surface composition of Jupiter Trojans, to check whether the spectral characteristics of small/faint bodies are different from those of larger/brigther objects, and to look for spectral features of ices and/or organics. All the investigated bodies have featureless spectra and a spectral behavior typical of the primitive P and D taxonomic classes. In particular, no signatures of water ice have been found on the spectra of these primordial bodies. From our investigation, the L4 and L5 clouds appear to be compositionally indistinguishable. Tentative models of the surface composition are presented and discussed.