The first lecture is devoted to an historical review of the developments of the teletherapy techniques which make use of hadron beams and are collectively called “hadrontherapy”. The main emphasis is on the use of protons and light ions, but also neutrons, pions and antiprotons are considered. The second lecture reviews the rationale behind the use of carbon ions in the treatment of radioresistant tumours and the results obtained both with proton and carbon ion beams on the 60 000 patients treated worldwide. The numbers of patients who would profit from hadrontherapy are presented together with the current landscape of running and planned hospital based centres. The main technical challenges set by this therapeutic modality are discussed in the third lecture together with the approaches either adopted or suggested to face them. The challenges are the treatment of moving organs, the development of new tools for Quality Assurance, the design of rotating gantries for carbon ions. The last discussed issue concerns the conception and realization of novel accelerators, better adapted to hadrontherapy than cyclotrons and synchrotrons.