With about 2000 exoplanets discovered within a large range of different configurations of distance from the star, size, mass, and atmospheric conditions, the concept of habitability cannot rely only on the stellar effective temperature anymore. In addition to the natural evolution of habitability with the intrinsic stellar parameters, tidal, magnetic, and atmospheric interactions are believed to
... [Show full abstract] have strong impact on the relative position of the planets inside the so-called habitable zone. Moreover, the notion of habitability itself strongly depends on the definition we give to the term “habitable”. The aim of this contribution is to provide a global and up-to-date overview of the work done during the last few years about the description and the modelling of the habitability, and to present the physical processes currently includes in this description.