Lunar based telescopes and observatories can provide a long term multi-wavelength window on the Universe. We discuss some basic constraints and specific facts regarding the use of the Moon as a site for astronomy and space science. We assess for this use the effects of gravity, rotation period, surface curvature, the seismic and tidal stability, as well as the tenuous atmosphere, temperature variations, weak magnetic fields on the Moon, micro meteorites flux and the properties of the regolith. We discuss the thermal and electromagnetic environments on the Moon and the properties of the dark lunar sites for astronomical instruments. The interest of polar lunar observatories (with eventual ice existence), the coldest sites in the solar system, is also presented. We then summarise the respective advantages and drawbacks of Moon-based astronomy and space science in relation to ground based and near-Earth orbit astronomy. Finally, we discuss the science of the Moon. We argue for the renewed interest of lunar exploration using advanced technologies for understanding the Earth/Moon history. The Moon is described as a test-bed for solar system exploration. It allows both remote and in-situ measurements for ground-truth validation of the understanding of other solar-system bodies.