Since planets were first discovered outside our own Solar System in 1992 (around a pulsar) and in 1995 (around a main sequence star), extrasolar planet studies have become one of the most dynamic research fields in astronomy. Now that more than 400 exoplanets have been discovered, focus has moved from finding planets to characterise these alien worlds. As well as detecting the atmospheres of these exoplanets, part of the characterisation process undoubtedly involves the search for extrasolar moons. This book develops these topics presenting data from NASA Space Missions such as Spitzer and Kepler. Moreover, it presents the current situation of the search for extraterrestrial life, both within and beyond the Solar System, detailing in particular the markers for the presence of life, the so called biosignatures. The dissertation should be especially useful to students and researchers in astronomical subjects but it could be found of great interest even by the curious of the night sky.