Nuclear pore complexes mediate the rapid trafficking of target macromolecules between the nucleus and the cytoplasm but exclude non-targets. Mathematical modeling helps to define the physical properties of a transport medium that can selectively enhance the permeation of some molecules but block others. Recent pioneering work has established a basis for quantitative modeling of nuclear translocation, and we expect this field to expand rapidly. A second area where modeling of nucleocytoplasmic transport has been prominently employed is in efforts to understand the regulatory networks by which signals pass between the nuclear and cytoplasmic compartments. Recent evidence suggests that the distinctive kinetics and spatial organization of nuclear transport processes can be used to efficiently propagate signals by new and unexpected pathways.