Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the applicative potential and in the perspective to investigate novel regimes as available laser intensities will be increasing. Experiments have demonstrated, over 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. An overview is given of the state of the art of ion acceleration by laser pulses as well as an outlook on its future development and perspectives. 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 are described.