Nuclear transport receptor that mediates nuclear import of proteins, such as histones, RPS3A, TNP2 and VDR (PubMed:11823430, PubMed:16207705, PubMed:17682055, PubMed:21454524). Serves as receptor for nuclear localization signals (NLS) in cargo substrates (PubMed:11823430, PubMed:16207705). Is thought to mediate docking of the importin/substrate complex to the nuclear pore complex (NPC) through binding to nucleoporin and the complex is subsequently translocated through the pore by an energy requiring, Ran-dependent mechanism (PubMed:11823430, PubMed:16207705). At the nucleoplasmic side of the NPC, Ran binds to the importin, the importin/substrate complex dissociates and importin is re-exported from the nucleus to the cytoplasm where GTP hydrolysis releases Ran (PubMed:11823430). The directionality of nuclear import is thought to be conferred by an asymmetric distribution of the GTP- and GDP-bound forms of Ran between the cytoplasm and nucleus (PubMed:11823430). Mediates the nuclear import of the histone H3-H4 dimer when in complex with ASF1 (ASF1A or ASF1B) (PubMed:21454524, PubMed:29408485). Mediates the ligand-independent nuclear import of vitamin D receptor (VDR) (PubMed:16207705). In vitro, mediates the nuclear import of human cytomegalovirus UL84 by recognizing a non-classical NLS (PubMed:12610148).