Kidney dialysis evolves as we learn more about the uremic condition. At its earliest versions the major transport process was diffusion, the spontaneous movement of particles down a concentration gradient, stimulated by thermal agitation, and affected by the collision of the particles with each other and with barriers such as dialysis membrane pore side walls. As dialysis was utilized to replace kidney function ultrafiltration (UF) was required, which could be generated by osmotic, oncotic, or hydrostatic pressures. Consequently, solvent drag effects of the UF led to an appreciation of the importance of convective transport and its advantageous property of increasing the removal of larger molecular sized (molecular weight + steric hindrance effects) species. Thus, modern dialysis generally utilizes both diffusive and convective transport and current devices and equipment allow for either process to occur independently or in combination. However, during convection solute is removed but concentrations in the retentate may not decrease unless substitution fluid is administered, a process called hemofiltration. Diffusion can occur without any UF. Appreciation of these extremes is important to the understanding of modern dialysis. Currently, dialysis cannot replace the endocrine or metabolic functions of the kidney so our discussion will be restricted to solute and fluid removal.