In the winter of 1868/9 the young Swiss doctor Friedrich Miescher, working in the laboratory of Felix Hoppe-Seyler at the University of Tübingen, performed experiments on the chemical composition of leukocytes that lead to the discovery of DNA. In his experiments, Miescher noticed a precipitate of an unknown substance, which he characterised further. Its properties during the isolation procedure and its resistance to protease digestion indicated that the novel substance was not a protein or lipid. Analyses of its elementary composition revealed that, unlike proteins, it contained large amounts of phosphorous and, as Miescher confirmed later, lacked sulphur. Miescher recognised that he had discovered a novel molecule. Since he had isolated it from the cells' nuclei he named it nuclein, a name preserved in today's designation deoxyribonucleic acid. In subsequent work Miescher showed that nuclein was a characteristic component of all nuclei and hypothesised that it would prove to be inextricably linked to the function of this organelle. He suggested that its abundance in tissues might be related to their physiological status with increases in "nuclear substances" preceding cell division. Miescher even speculated that it might have a role in the transmission of hereditary traits, but subsequently rejected the idea. This article reviews the events and circumstances leading to Miescher's discovery of DNA and places them within their historic context. It also tries to elucidate why it was Miescher who discovered DNA and why his name is not universally associated with this molecule today.