Ion acceleration from solid targets irradiated by high-intensity pulses is a burgeoning area of research, currently attracting large interest worldwide. The properties of laser-driven ion beams (high brightness and laminarity, high-energy cut-off, ultrashort burst duration) are, in several respects, markedly different from those of 'conventional' accelerator beams. In view of these properties, laser-driven ion beams have the potential to be employed in a number of innovative applications in the scientific, technological and medical areas. The scope of this paper is to briefly review the state of the art in this area and discuss in this context some recent results obtained by our group and collaborators, aimed at studying the acceleration mechanism, optimizing the source properties and applying the beams as a diagnostic tool in scientific experiments. An application that has already produced important results is the use of laser-accelerated protons as a particle probe for the detection of electric and magnetic fields in plasmas. Examples of these results will be presented and discussed.