Spectroscopic observations performed during a planetary transit can reveal spectral features in absorption on the continuum background of the parent star, allowing thus direct studies of exoplanets atmospheres. We performed such observations with the Hubble Space Telescope, that allowed evaporation of hot Jupiters to be constrained. I will present the observations and corresponding models. First, we reported the discovery of escaping hydrogen in the extended atmosphere of HD209458b. Subsequent observations confirmed the escape and even more, they allowed the detection of oxygen and carbon, showing that the escape mechanism is not a pure Jeans' escape but an hydrodynamical blow-off. New observations are now available in order to put additional constraints. To interpret the observations, we developed models that allow physical parameters to be derived for exoplanets, including temperatures, densities, escaping rates or life times. The results nicely fit the observational estimates of the escape rate from HD209458b. Moreover, they may explain the lack of low-mass planets with short orbital distances. As those planets might efficiently evaporate, we infer the existence of a new kind of planets, made of the residual core of former hot Jupiters.