Abstract. DNA damage caused by irradiation has been studied for many decades. Such studies allow us to better assess the dangers posed by radiation, and to increase the efficiency of the radiotherapies that are used to combat cancer. A full description of the irradiation process involves multiple size and time scales. It starts from the interaction of radiation -either photons or swift ions -with the biological medium. Such interactions cause electronic excitation and ionisation. The two main products of ionising radiation are thus electrons and radicals. Both of these species can cause damage to biological molecules, in particular DNA. In the long run, this molecular level damage can prevent cells from replicating and can hence lead to cell death. For a long time it was assumed that the main actors in the damage process were the radicals. However, experiments in a seminal paper by the group of Leon Sanche in 2000 showed that low-energy electrons (LEE), such as those generated when ionising biological targets, can also cause bond breaks in biomolecules, in particular strand breaks in plasmid DNA [1]. These results prompted a significant amount of experimental and theoretical work aimed at elucidating the role played by LEE in DNA damage.In this Topical Review we provide a general overview of the problem. We discuss experimental findings and theoretical results hand in hand with the aim of describing the physics and chemistry that occurs during the process of radiation damage, from the initial stages of electronic excitation, through the inelastic propagation of electrons in the medium, the interaction of electrons with DNA, and the chemical end-point effects on DNA. A very important aspect of this discussion is the consideration of a realistic, physiological environment. The role played by the aqueous solution and the amino acids from the histones in chromatin must be considered. Moreover, thermal fluctuations must be incorporated when studying these phenomena. Hence, a special place in this Topical Review is occupied by our recent first-principles molecular dynamics simulations that address the issue of how the environment favours or prevents LEEs from causing damage to DNA. We finish by summarising the conclusions achieved so far, and by suggesting a number of possible directions for further study.