During the last two decades it became clear that a significant fraction of the biological cellular damage caused by high-energy radiation is actually due to reactions induced by low-energy electrons (<20 eV). In this energy regime electrons can efficiently decompose molecules such as DNA or DNA building blocks by dissociative electron attachment (DEA) . Experiments on single DNA building blocks have been performed in the gas phase revealing that DEA can proceed with remarkable site selectivity. Low-energy electron-induced DNA strand breakage is typically investigated using plasmid DNA in the condensed phase. Very recently, a pronounced dependence of electron induced DNA strand breakage on the nucleotide sequence was found using different experimental approaches suggesting that at least part of the observed strand breaks are due to initial electron attachment to the nucleobases . Currently, a strong research focus is on the fundamental understanding of DEA to therapeutically administered radiosensitizers. In the near future DEA to novel potential radiosensitizers will be explored, and the electron induced damage of biomolecules within complex environments has to be investigated. Considerable attention has been paid to the theoretical research of the DEA in the context of the DNA damage. With respect to this, the theoretical part of the chapter reviews all the computational approaches that have been used to study DEA to biomolecules over the last decade. These approaches are divided into two classes. The first class consists of electronic structure methods studying the transient negative ions formed by electrons captured by the neutral building blocks of the DNA. Approaches dealing with the complicated nuclear dynamics of the DEA to biomolecules form the second class explored in this chapter.