We discuss the evolution of the habitable zone around low mass and intermediate mass stars as they evolve off the main sequence. This work shows that this class of stars should be included in the search for life because if planets could be found in their habitable zones, they will allow to test different hypothesis concerning the conditions of life formation. For instance if these planets show traces for life, it is possible to empirically determine a lower limit to the timescale for the formation of life. This time scale is not well determined from the Earth's study, as life formation initially occurred during a period of heavy bombardment from comets and asteroids during the formation of the solar system. We will summarize (to the best of our knowledge) some of the recent results concerning the early signs of life on Earth. We will present some of our work in progress in which we evaluate the effects of stellar evolution on the habitable zone changes.