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”. To establish neutrino astronomy beyond the detection of single events, neutrino telescopes of km3 scale are needed. In order to obtain full sky coverage, a corresponding detector in the Mediterranean Sea is required to complement the IceCube experiment currently under construction at the South Pole. The groups pursuing the current neutrino telescope projects in the Mediterranean Sea, ANTARES, NEMO and NESTOR, have joined to prepare this future installation in a 3-year, EU-funded design study named KM3NeT (in the following, this name will also denote the future detector). This report will highlight some of the physics issues to be addressed with KM3NeT and will outline the path towards its realisation, with a focus on the upcoming design study.