It has become increasingly apparent in recent years that next-generation sequencing (NGS) has a blind spot for large scale genomic variation, which is crucial for understanding the genotype-phenotype relationship. Genomic mapping methods attempt to overcome the weakesses of NGS by providing a coarse-grained map of the distances between restriction sites to aid in sequence assembly. From such methods, one hopes to realize fast and inexpensive <italic>de novo</italic> sequencing of human and plant genomes.One of the most promising methods for genomic mapping involves placing DNA inside a device only a few dozen nanometers wide called a nanochannel. A nanochannel stretches the DNA so that the distance between fluorescently labeled restriction sites can be measured en route to obtaining an accurate genome map. Unfortunately for those who wish to design devices, the physics of how DNA stretches when confined in a nanochannel is still an active area of research. Indeed, despite decades old theories from polymer physics regarding weakly and strongly stretched polymers, seminal experiments in the mid-2000s have gone unexplained until very recently.With a goal of creating a realistic engineering model of DNA in nanochannels, this dissertation addresses a number of important outstanding research topics in this area. We first discuss the physics of dilute solutions of DNA in free solution, which show distinctive behavior due to the stiff nature of the polymer. We then turn our attention to the equilibrium regimes of confined DNA and explore the effects of stiff chains and weak excluded volume on the confinement free energy and polymer extension. We also examine dynamic properties such as the diffusion coefficient and the characteristic relaxation time. Finally, we discuss a sister problem related to DNA confined in nanoslits, which shares much of the same physics as DNA confined in channels.Having done this, we find ourselves with a well-parameterized wormlike chain model that is remarkably accurate in describing the behavior of DNA in confinement. As such, it appears that researchers may proceed with the rational design of nanochannel mapping devices using this model.