Transport in liquid-filled pores of molecular dimensions plays an important role in membrane separations, in various forms of chromatography, and in catalysis, to name a few examples. A frequent observation is that if the pore dimensions are of the same order as those of a solute molecule, the apparent diffusion coefficient of that solute is much lower than in bulk solution. Likewise, rates of convective transport of such solutes are generally lower than the product of bulk concentration and volume flow rate. Thus, solute transport is typically “hindered” or restricted. A key objective of research on hindered transport is to be able to predict the applicable transport coefficients from such fundamental information as the size, shape, and electrical charge of the solutes and pores. The present status of this research is reviewed.