The observation of high-energy extraterrestrial neutrinos is one of the most promising future options to increase our knowledge on non-thermal processes in the universe. Neutrinos are e.g. unavoidably produced in environments where high-energy hadrons collide; in particular this almost certainly must be true in the astrophysical accelerators of cosmic rays, which thus could be identified unambiguously by sky observations in neutrino light. On the one hand, neutrinos are ideal messengers for astrophysical observations since they are not deflected by electromagnetic fields and interact so weakly that they are able to escape even from very dense production regions and traverse large distances in the universe without attenuation. On the other hand, their weak interaction poses a significant problem for detecting neutrinos. Huge target masses up to gigatons must be employed, requiring to instrument natural abundances of media such as sea water or antarctic ice. The first generation of such neutrino telescopes is taking data or will do so in the near future, while the second-generation projects with cubic-kilometre size is under construction or being prepared. This report focuses on status and prospects of current (ANTARES, NEMO, NESTOR) and future (KM3NeT) neutrino telescope projects in the Mediterranean Sea.