This brief provides an in-depth overview of the physics of hadron therapy, ranging from the history to the latest contributions to the subject. It covers the mechanisms of protons and carbon ions at the molecular level (DNA breaks and proteins 53BP1 and RPA), the physics and mathematics of accelerators (Cyclotron and Synchrotron), microdosimetry measurements (with new results so far achieved), and Monte Carlo simulations in hadron therapy using FLUKA (CERN) and MCHIT (FIAS) software. The text also includes information about proton therapy centers and carbon ion centers (PTCOG), as well as a comparison and discussion of both techniques in treatment planning and radiation monitoring. This brief is suitable for newcomers to medical physics as well as seasoned specialists in radiation oncology.