The relative simplicity of viruses makes it possible to apply generic physical approaches to the understanding of their structure and function. We focus here on viruses that have double-stranded (ds)DNA genomes that are enclosed in a protein container called the capsid. Their structures are now known in precise detail from cryo-electron microscopy. dsDNA is a stiff, highly charged polymer, and typical viral DNAs have contour lengths 1000 times longer than the radius of the capsid into which they are introduced in the assembly process, which is driven by a biological motor. As a result, the confined DNA is highly stressed. The energy stored in the dsDNA, which is compressed to crystalline densities, drives the ejection of the genome into the host at the start of an infection. Experiments have examined the packaging and ejection of the genomes, which have also been the subject of analytic theories and simulations.