ELI-Beamlines is one of the four pillars of the ELI (Extreme Light Infrastructure) pan-European project. It will be an ultrahigh-intensity, high repetition-rate, femtosecond laser facility whose main goal is to generate and apply high-brightness X-ray sources and accelerated charged particles. In particular, medical applications are treated by the ELIMED task force, which has been launched by collaboration between ELI and INFN researchers. ELIMED aims to demonstrate the clinical applicability of laser accelerated ions. In this article, the state of the ELIMED project and the first scientific results are reported. The design and realisation of a preliminary beam handling system and of an advanced spectrometer for diagnostics of high energy (multi-MeV) laser-accelerated ion beams will also be briefly presented.