Laser accelerated proton beams have been proposed to be used in different research fields. A great interest has risen for the potential replacement of conventional accelerating machines with laser-based accelerators, and in particular for the development of new concepts of more compact and cheaper hadrontherapy centers. In this context the ELIMED (ELI MEDical applications) research project has been launched by INFN-LNS and ASCR-FZU researchers within the pan-European ELI-Beamlines facility framework. The ELIMED project aims to demonstrate the potential clinical applicability of optically accelerated proton beams and to realize a laser-accelerated ion transport beamline for multi-disciplinary user applications. In this framework the eye melanoma, as for instance the uveal melanoma normally treated with 62 MeV proton beams produced by standard accelerators, will be considered as a model system to demonstrate the potential clinical use of laser-driven protons in hadrontherapy, especially because of the limited constraints in terms of proton energy and irradiation geometry for this particular tumour treatment. Several challenges, starting from laser-target interaction and beam transport development up to dosimetry and radiobiology, need to be overcome in order to reach the ELIMED final goals. A crucial role will be played by the final design and realization of a transport beamline capable to provide ion beams with proper characteristics in terms of energy spectrum and angular distribution which will allow performing dosimetric tests and biological cell irradiation. A first prototype of the transport beamline has been already designed and other transport elements are under construction in order to perform a first experimental test with the TARANIS laser system by the end of 2013. A wide international collaboration among specialists of different disciplines like Physics, Biology, Chemistry, Medicine and medical doctors coming from Europe, Japan, and the US is growing up around the ELIMED project with the aim to work on the conceptual design, technical and experimental realization of this core beamline of the ELI Beamlines facility.