Abstract The continuing development of powerful laser systems has permitted to extend the interaction of laser beams with matter far into the relativistic domain in which extremely high electric and magnetic fields are generated. Thanks to these tremendous fields, that only plasma can support and sustain, new and compact approaches for producing energetic particle beams have been recently achieved. The incredible progress of these laser–plasma accelerators has allowed physicists to produce high quality beams of energetic radiation and particles. These beams have interesting properties such as shortness, brightness and spatial quality, and could lend themselves to applications in many fields, including medicine (radiotherapy, proton therapy, imaging), radiation biology (short-time-scale), chemistry (radiolysis), physics and material science (radiography, electron and photon diffraction), security (material inspection), and of course accelerator science. Stimulated by the advent of compact and powerful lasers, with moderate costs and high repetition rate, this research field has witnessed considerable growth in the past few years, and the promises of laser–plasma accelerators are in tremendous progress. The recent years in particular have seen spectacular progress in the acceleration of electrons and of ions, both in terms of energy and in terms of quality of the beams. To cite this article: V. Malka, P. Mora, C. R. Physique 10 (2009).