Picking up at the conclusion of Viovy's review of the physics of gel electrophoresis [J.-L. Viovy, Rev. Mod. Phys. 72, 813 (2000)], this review synthesizes the experimental data, theoretical models, and simulation results for DNA electrophoresis in microfabricated and nanofabricated devices appearing since the seminal paper by Volkmuth and Austin [Nature (London) 358, 600 (1992)]. Prototype versions of these devices separate DNA by molecular weight at a rate far superior to gel electrophoresis. After providing an overview of the requisite background material in polymer physics, electrophoresis, and microfluidic device fabrication, the focus is on the following three generic problems: (i) collision with an isolated post, (ii) transport in an array of posts, and (iii) entropic trapping and filtration in the slit-well motif. The transport phenomena are examined here in the context of the length and time scales characterizing the DNA, the device, and the applied electric field.