Active transport of proteins and RNAs between the nucleus and cytoplasm is a major process in eukaryotic cells. Recently, factors that recognize transport substrates and mediate nuclear import or export have been characterized, revealing interactions that target substrates to the nuclear pore complexes, through which translocation occurs. Translocation requires energy, and for the import process this energy is at least partly consumed by the action of the small guanosine triphosphatase Ran. In the first half of the review, some of the well-established general background information on nucleocytoplasmic transport is discussed. The second half describes recent information on the mechanistic details of nuclear import and export as well as major unresolved issues such as how directionality is conferred on either import or export. The whole review is slanted toward discussion of metazoan cells.