Size-based DNA separation is at the heart of numerous biological applications. While gel electrophoresis remains widely utilized to fractionate DNA according to their size, the method has several shortcomings. Recent advances in micro- and nano-fabrication techniques engendered several microfabricated devices aimed at addressing some of the limitations of gel electrophoresis for DNA separations. In this thesis, we employ a combination of analytical and computational methods to characterize the electrophoretic motion of DNA molecules in microfabricated, confining geometries. In particular, we consider three situations: (i) the migration of short DNA in nanofilters (a succession of narrow slits, connecting deep wells) under a high electric field; (ii) the metastable unhooking of a long DNA chain wrapped around a cylindrical post; and (iii) the dynamics of long DNA chains in an array of spherical cavities connected by nanopores. We provide insights on the physical mechanisms underlying the transport of DNA in such geometries. Useful guidelines for the optimal design of new separation devices result from the fundamental understanding gained by the approach we propose.