Development of new radiotherapy strategies based on the use of hadrons, as well as reduction of uncertainties associated with radiation health risk during long-term space flights, requires increasing knowledge of the mechanisms underlying the biological effects of charged particles. It is well known that charged particles are more effective in damaging biological systems than photons. This capability has been related to the production of spatially correlated and/or clustered DNA damage, in particular two or more double-strand breaks (DSB) in close proximity or DSB associated with other lesions within a localized DNA region. These kinds of complex damages are rarely induced by photons. They are difficult to repair accurately and are therefore expected to produce severe consequences at the cellular level. This paper provides a review of radiation-induced cellular effects and will discuss the dependence of cell death and mutation induction on the linear energy transfer of various light and heavy ions. This paper will show the inadequacy of a single physical parameter for describing radiation quality, underlining the importance of the characteristics of the track structure at the submicrometer level to determine the biological effects. This paper will give a description of the physical properties of the track structure that can explain the differences in the spatial distributions of DNA damage, in particular DSB, induced by radiation of different qualities. In addition, this paper will show how a combined experimental and theoretical approach based on Monte Carlo simulations can be useful for providing information on the damage distribution at the nanoscale level. It will also emphasize the importance, especially for DNA damage evaluation at low doses, of the more recent functional approaches based on the use of fluorescent antibodies against proteins involved in the cellular processing of DNA damage. Advantages and limitations of the different experimental techniques will be discussed with particular emphasis on the still unsolved problem of the clustered DNA damage resolution. Development of biophysical models aimed to describe the kinetics of the DNA repair process is underway, and it is expected to support the experimental investigation of the mechanisms underlying the cellular radiation response.