Nucleocytoplasmic transport is mediated by shuttling receptors that recognize specific signals on protein or RNA cargoes and translocate the cargoes through the nuclear pore complex. Transport receptors appear to move through the nuclear pore complex by facilitated diffusion, involving repeated cycles of binding to and dissociation from nucleoporins with phenylalanine-glycine motifs. We discuss recent experimental approaches and results that have begun to provide molecular insight into the mechanisms by which transport complexes traverse the nuclear pore complex, and point out the significant gaps in understanding that remain.