We overview our recent theoretical predictions and the innovative experimental findings that inspired us concerning the mechanisms by which very low-energy (0.1-2 eV) free electrons attach to DNA and cause strong (ca. 4 eV) covalent bonds to break causing so-called single-strand breaks. Our primary conclusions are that (i) attachment of electrons in the above energy range to base pi* orbitals is more likely than attachment elsewhere and (ii) attachment to base pi* orbitals most likely results in cleavage of sugar-phosphate C-O sigma bonds. Later experimental findings that confirmed our predictions about the nature of the electron attachment event and about which bonds break when strand breaks form are also discussed. The proposed mechanism of strand break formation by low-energy electrons involves an interesting through-bond electron-transfer process.