Nucleocytoplasmic transport, the exchange of matter between nucleus and cytoplasm, plays a fundamental role in human and other eukaryotic cells, affecting almost every aspect of health and disease. The only gate for the transport of small and large molecules as well as supramolecular complexes between nucleus and cytoplasm is the nuclear pore complex (NPC). The NPC is not a normal membrane transport protein (transporter). Composed of 500 to 1000 peptide chains, the NPC features a mysterious functional duality. For most molecules, it constitutes a molecular sieve with a blurred cutoff at approx 10 nm, but for molecules binding to phenylalanine-glycine (FG) motifs, the NPC appears to be a channel of approx 50 nm diameter, permitting bidirectional translocation at high speed. To achieve this, the NPC cooperates with soluble factors, the nuclear transport receptors, which shuttle between nuclear contents and cytoplasm. Here, we provide a short introduction to nucleocytoplasmic transport by describing first the structure and composition of the nuclear pore complex. Then, mechanisms of nucleocytoplasmic transport are discussed. Finally, the still essentially unresolved mechanisms by which nuclear transport receptors and transport complexes are translocated through the nuclear pore complex are considered, and a novel translocation model is suggested.