Nanofluidic structures have over the last two decades emerged as a powerful platform for detailed analysis of DNA on the kilobase pair length scale. When DNA is confined to a nanochannel, the combination of excluded volume and DNA stiffness leads to the DNA being stretched to near its full contour length. Importantly, this stretching takes place at equilibrium, without any chemical modifications to the DNA. As a result, any DNA can be analyzed, such as DNA extracted from cells or circular DNA, and it is straight-forward to study reactions on the ends of linear DNA. In this comprehensive review, we first give a thorough description of the current understanding of the polymer physics of DNA and how that leads to stretching in nanochannels. We then describe how the versatility of nanofabrication can be used to design devices specifically tailored for the problem at hand, either by controlling the degree of confinement or enabling facile exchange of reagents to measure DNA-protein reaction kinetics. The remainder of the review focuses on two important applications of confining DNA in nanochannels. The first is optical DNA mapping, which provides the genomic sequence of intact DNA molecules in excess of 100 kilobase pairs in size, with kilobase pair resolution, through labeling strategies that are suitable for fluorescence microscopy. In this section, we highlight solutions to the technical aspects of genomic mapping, including the use of enzyme-based labeling and affinity-based labeling to produce the genomic maps, rather than recent applications in human genetics. The second is DNA-protein interactions, and several recent examples of such studies on DNA compaction, filamentous protein complexes, and reactions with DNA ends are presented. Taken together, these two applications demonstrate the power of DNA confinement and nanofluidics in genomics, molecular biology, and biophysics.