Low-energy electrons (LEEs) of energies ≤30 eV are generated in large quantities by ionizing radiation. These electrons can damage DNA; particularly, they can induce the more detrimental clustered lesions in cells. This type of lesions, which are responsible for a large portion of the genotoxic stress generated by ionizing radiation, is described in the Introduction. The reactions initiated by the collisions of 0.5–30 eV electrons with oligonucleotides, duplex DNA, and DNA bound to chemotherapeutic platinum drugs are explained and reviewed in the subsequent sections. The experimental methods of LEE irradiation and DNA damage analysis are described with an emphasis on the detection of cluster lesions, which are considerably enhanced in DNA–Pt–drug complexes. Based on the energy dependence of damage yields and cross-sections, a mechanism responsible for the clustered lesions can be attributed to the capture of a single electron by the electron affinity of an excited state of a base, leading to the formation of transient anions at 6 and 10 eV. The initial capture is followed by electronic excitation of the base and dissociative attachment—at other DNA sites—of the electron reemitted from the temporary base anion. The mechanism is expected to be universal in the cellular environment and plays an important role in the formation of clustered lesions.