The astrophysical and physical processes at the very end of the known energy spectrum, in the region of the so-called Ultra High Energies (UHE), have been the subject of an intense debate in the last years. UHE particles are nucleons, nuclei, photons, and neutrinos or even new particles predicted by theory, but not discovered yet, with energies from a few $10^18$ eV, where fluxes of cosmic neutrinos are expected from "standard" physics and astrophysics, to beyond the decade of $10^0$ eV, where radiation is thought to be produced under the most extreme physical conditions in the Universe. The understanding of the nature, origin, propagation to Earth of such UHE particles would provide entire new information on the sources and the astrophysical mechanisms that could produce them. Moreover, observations at UHE, would, possibly, allow us to test high energy physics beyond the limit of existing and next generation accelerators as well as Lorentz invariance at extreme energies. The ground-based Pierre Auger Observatory, whose southern site is currently being completed in Argentina, will surely provide, in the near future, more solid observational bases for the understanding of what is today the UHE puzzle. However, in any post-Auger scenario, only space-based observatories can reach the collecting power necessary to fully explore the UHE Universe, establishing then "Particle Astronomy" as a new observational window. Building on the studies conducted for the ESA-led Mission EUSO, we summarize here: 1. the science goals of an ESA "Cosmic Vision 2015- 2025" mission for UHE search; 2. Its scientific requirements; 3. The necessary R&D preliminary to any further development of such a challenging innovative mission.