Trojan asteroids located in the Jupiter Lagrangian points L4 and L5 (60 degrees ahead and behind Jupiter) are widely believed to be primordial bodies since their orbits are stable over the age of the Solar System. They seem to have been formed in a region of the solar nebula rich in frozen volatiles and to have never suffered selective induction heating. They probably still contain ices in their interiors.Moreover the discovery of several dynamical families among Trojans suggests that they are at least as collisionally evolved as the main asteroid belt. Since 2002, we started an observational program on Jupiter Trojans at ESO-NTT, ESO-VLT and TNG. In particular we concentrated on members of dynamical families, as defined by Beauge and Roig (2001), and we observed also several background objects. We carry out visible and near-infrared spectroscopy and photometry in order to i) characterize the mineralogical composition of families, ii) give evidence of ongoing space weathering, and iii) confirm family membership. As expected, the spectra of the non-family members are more heterogeneous compared to the spectra of family members. The obtained results will be presented and discussed.