Deeply understanding the basic mechanisms of radiation damage in vitro and on living cells, starting from the early radical and molecular processes to mutagenic DNA lesions, cell signalling, genomic instability, apoptosis, microenvironment and Bystander effects, radio sensitivity should have many practical consequences such as the customization of cancer radiotherapy or radioprotection protocols. In this context, innovative laser–plasma accelerators provide ultra-short particle beams (electrons, protons) with parameters of interest for radiation biology and medical physics. This review article approaches some complex links that exist between radiation physics of new pulsed irradiation sources and potential biomedical applications. These links concern mainly the understanding of spatio-temporal events triggered by a radiation, within a fluctuating lapse of time from the initial energy deposition to primary damages of biological interest.