C. Dumas (ESO), F. Merlin, A. Barucci, C. deBergh, A. Guilbert, A. Doressoundiram (Obs. Paris-Meudon), O. Hainaut (ESO) Spectral modeling methods applied to the reflectance spectra of outer solar system bodies such as Trans-Neptunian Objects, is a powerful tool to establish an inventory of the icy compounds covering their surfaces, as well as to characterize their physical properties (abundance, temperature, mixing-ratio, phase) and the processes (bombardments, irradiation, cryo-volcanism) they have undergone since their accretion in the proto-planetary nebula. We'll present an overview of the latest observational and spectral modeling results concerning the surface composition of the largest TNOs, including the analysis of recent SINFONI spectroscopic data obtained at VLT Observatory for the TNOs 2003 UB313 (Eris) and 2003 EL61.