Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the potential for a number of foreseen applications and in the perspective to investigate novel regimes as far as available laser intensities will be increasing. Experiments have demonstrated in a wide range of laser and target parameters the generation of multi-MeV proton and ion beams with unique properties such as ultrashort duration, high brilliance and low emittance. In this paper we give an overview of the state-of-the art of ion acceleration by laser pulses as well as an outlook on its future development and perspectives. We describe the main features observed in the experiments, the observed scaling with laser and plasma parameters and the main models used both to interpret experimental data and to suggest new research directions.