Thanks to direct observation and manipulation of DNA in micro/nanofluidic devices, we are now able to elucidate the relationship between the polymer microstructure and its rheological properties, as well as to design new single-molecule platforms for biophysics and biomedicine. This allows exploration of many new mechanisms and phenomena, which were previously unachievable with conventional methods such as bulk rheometry tests. For instance, the field of polymer rheology is at a turning point to relate the complex molecular conformations to the nonlinear viscoelasticity of polymeric fluids (such as coil-stretch transition, shear thinning, and stress overshoot in startup shear). In addition, nanofluidic devices provided a starting point for manipulating single DNA molecules by applying basic principles of polymer physics, which is highly relevant to numerous processes in biosciences. In this article, we review recent progress regarding the flow and deformation of DNA in micro/nanofluidic systems from both fundamental and application perspectives. We particularly focus on advances in the understanding of polymer rheology and identify the emerging research trends and challenges, especially with respect to future applications of nanofluidics in the biomedical field.