Various materials are presently available for hollow fiber dialysis membranes which satisfy technical and medical requirements such as high permeability to uremic toxins and water, biocompatibility, resistance to sterilization, and high mechanical strength. New dialysis membranes with high permeability to β2-microglobulin and with biocompatibility leading to low complement activation have been developed for more optimal hemodialysis. Data on structure and permeability are then required to prepare the new dialysis membranes. Much attention should be paid also to the geometry of hollow fiber dialysis membranes available for chronic renal failure patients with elevated hematocrits caused by the administration of erythropoietin.