DNA and RNA are the most individual molecules known. Therefore, single-molecule experiments with these nucleic acids are particularly useful. This review reports on recent experiments with single DNA and RNA molecules. First, techniques for their preparation and handling are summarised including the use of AFM nanotips and optical or magnetic tweezers. As important detection techniques, conventional and near-field microscopy as well as fluorescence resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) are touched on briefly. The use of single-molecule techniques currently includes force measurements in stretched nucleic acids and in their complexes with binding partners, particularly proteins, and the analysis of DNA by restriction mapping, fragment sizing and single-molecule hybridisation. Also, the reactions of RNA polymerases and enzymes involved in DNA replication and repair are dealt with in some detail, followed by a discussion of the transport of individual nucleic acid molecules during the readout and use of genetic information and during the infection of cells by viruses. The final sections show how the enormous addressability in nucleic acid molecules can be exploited to construct a single-molecule field-effect transistor and a walking single-molecule robot, and how individual DNA molecules can be used to assemble a single-molecule DNA computer.