The shortcomings of diffusion as a mechanism of glucose transfer across cell membranes date back to the last century. The early work, mostly qualitative, was greatly extended by LeFevre in America and by Wilbrandt in Switzerland, who reported their quantitative studies at the Bangor Symposium of The Society of Experimental Biology in 1953 (LeFevre, 1954; Wilbrandt, 1954). Widdas (1952) published simple carrier kinetics for glucose transfer which predicted the phenomenon of uphill transfer by counterflow. However, in that 1952 paper it was carefully pointed out that a good fit to the kinetics did not define the details of the mechanism. Nevertheless, the reverse is true: namely, any viable scheme of working must be consistent with the established kinetic properties. For instance the kinetics of uphill transfer by counterflow (confirmed four years later by Park, Post, Kalman, Wright, Johnson & Morgan, 1956; Rosenherg & Wilbrandt, 1957) clearly exclude a simple water channel through the membrane.The concept of a mobile membrane carrier on which the early kinetics were based was variously modified to meet newer developments, which included asymmetric affinities on the outside and inside of the red cell membrane. The mobile carrier has now been superseded by the concept of membrane protein transporters. Nevertheless, some of the nomenculture, such as carrier transport and carrier catalysis (Krämer, 1994), has persisted although it no longer conveys all the subtleties of the transfer mechanism.