A comprehensive understanding of sub-stellar objects (brown dwarfs and extrasolar giant planets) and their population characteristics (e.g. IMF, formation history) is only possible through the robust interpretation of ultra-cool objects spectroscopy. However, the physics of ultra-cool atmospheres is complicated by a variety of challenging ingredients (dust properties, non-equilibrium chemistry, molecular opacities). Moreover, while hydrogen-burning stars stabilize on the stellar main-sequence, sub-stellar objects continuously cool down (since they lack an internal source of energy) and evolve towards later spectral types. Their atmospheric parameters are a strong function of age. In this talk I will present the spectroscopic analysis of a large sample of L and T dwarfs, complementing the spectroscopic data with astrometry from the PARSEC program, in order to constrain the sub-stellar initial mass function and formation history. I will then describe our new effort to identify and characterize a large sample of benchmark systems, combining Gaia capabilities with large area near-infrared surveys such as UKIDSS, SDSS, and VVV, in order to calibrate effectively the theoretical models.