A review of the mathematical modeling of axial-flow hollow fiber cell bioreactors is presented. The models cover the range of diffusion-limited to convective-flow dominant nutrient transport conditions. Mass transport limitations inherent in the axial-flow bioreactor design are illustrated with model calculations. Simulation results further demonstrate the importance of convective nutrient transport to the cell growth region. These model developments were restricted to the transport and consumption of small substrate molecules in dilute solution. Finally, convection-enhanced hollow fiber bioreactor designs and alternative schemes for operating axial-flow bioreactors are discussed.