Summarizing we can state that the HZ is the range of orbital distances from a star, in which a planet can maintain liquid water and biological productivity on its surface. The HZ can be calculated with the help of climatological approaches or within the frame- work of Earth system science. According to our model, the HZ for the present solar system extends between about 0.95 AU and about 1.2 AU  and was broader in the past. For extrasolar systems we can postulate a distinct HZ for young central stars in the mass range between about 0.4 and 2 solar masses. The next two parts describe model calculations for the Sun and for other single main sequence stars, respectively. In the final we give our main conclusions and point out several areas for future work. 3.1 Models for Calculating the HZ in the Solar System Since the early work of Hart [9, 10], there have been many improvements in climatic constraints on the inner and outer boundaries of the HZ. The most comprehensive work in this field is the paper by Kasting et al. . The authors define the boundaries of the HZ via so-called critical solar fluxes. For the inner radius of the HZ they give three different estimations based on the following assumptions: 1. loss of planetary water by a moist greenhouse , 2. loss of planetary water by a runaway greenhouse, 3. observation that there was no liquid water on Venus‘ surface at least for the last 1 Ga.