Physically interesting behaviour can arise when soft matter is confined to nanoscale dimensions. A highly relevant biological example of such a phenomenon is the Nuclear Pore Complex (NPC) found perforating the nuclear envelope of eukaryotic cells. In the central conduit of the NPC, of ∼30-60 nm diameter, a disordered network of proteins regulates all macromolecular transport between the nucleus and the cytoplasm. In spite of a wealth of experimental data, the selectivity barrier of the NPC has yet to be explained fully. Experimental and theoretical approaches are complicated by the disordered and heterogeneous nature of the NPC conduit. Modelling approaches have focused on the behaviour of the partially unfolded protein domains in the confined geometry of the NPC conduit, and have demonstrated that within the range of parameters thought relevant for the NPC, widely varying behaviour can be observed. In this review, we summarise recent efforts to physically model the NPC barrier and function. We illustrate how attempts to understand NPC barrier function have employed many different modelling techniques, each of which have contributed to our understanding of the NPC.