Proteins are translated in the cytoplasm, but many need to access the nucleus to perform their functions. Understanding how these nuclear proteins are transported through the nuclear envelope and how the import processes are regulated is therefore an important aspect of understanding cell function. Structural biology has played a key role in understanding the molecular events during the transport processes and their regulation, including the recognition of nuclear targeting signals by the corresponding receptors. Here, we review the structural basis of the principal nuclear import pathways and the molecular basis of their regulation. The pathways involve transport factors that are members of the β-karyopherin family, which can bind cargo directly (e.g. importin-β, transportin-1, transportin-3, importin-13) or through adaptor proteins (e.g. importin-α, snurportin-1, symportin-1), as well as unrelated transport factors such as Hikeshi, involved in the transport of heat-shock proteins, and NTF2, involved in the transport of RanGDP. Solenoid proteins feature prominently in these pathways. Nuclear transport factors recognize nuclear targeting signals on the cargo proteins, including the classical nuclear localization signals (cNLSs), recognized by the adaptor importin-α, and the PY-NLSs, recognized by transportin-1. Post-translational modifications, in particular phosphorylation, constitute key regulatory mechanisms operating in these pathways.