AbstractIn the past 15 years, astronomers have revealed that a significant fraction of the stars should harbour planets and that it is likely that terrestrial planets are abundant in our galaxy. Among these planets, how many are habitable, i.e. suitable for life and its evolution? These questions have been discussed for years and we are slowly making progress. Liquid water remains the key criterion for habitability. It can exist in the interior of a variety of planetary bodies, but it is usually assumed that liquid water at the surface interacting with rocks and light is necessary for emergence of a life able to modify its environment and evolve. The first key issue is thus to understand the climatic conditions allowing surface liquid water assuming a suitable atmosphere. These have been studied with global mean one-dimensional (1D) models which have defined the ‘classical habitable zone’, the range of orbital distances within which worlds can maintain liquid water on their surfaces (Kasting et al. 1993). A new generation of 3D climate models based on universal equations and tested on bodies in the solar system are now available to explore with accuracy climate regimes that could locally allow liquid water. The second key issue is now to better understand the processes which control the composition and the evolution of the atmospheres of exoplanets, and in particular the geophysical feedbacks that seem to be necessary to maintain a continuously habitable climate. From that point of view, it is not impossible that the Earth's case may be special and uncommon.