Antifreeze proteins are characterised by their ability to prevent ice from growing upon cooling below the bulk melting point. This displacement of the freezing temperature of ice is limited and at a sufficiently low temperature a rapid ice growth takes place. The separation of the melting and freezing temperature is usually referred to as thermal hysteresis, and the temperature of ice growth is referred to as the hysteresis freezing point. The hysteresis is supposed to be the result of an adsorption of antifreeze proteins to the crystal surface. This causes the ice to grow as convex surface regions between adjacent adsorbed antifreeze proteins, thus lowering the temperature at which the crystal can visibly expand. The model requires that the antifreeze proteins are irreversibly adsorbed onto the ice surface within the hysteresis gap. This presupposition is apparently in conflict with several characteristic features of the phenomenon; the absence of superheating of ice in the presence of antifreeze proteins, the dependence of the hysteresis activity on the concentration of antifreeze proteins and the different capacities of different types of antifreeze proteins to cause thermal hysteresis at equimolar concentrations. In addition, there are structural obstacles that apparently would preclude irreversible adsorption of the antifreeze proteins to the ice surface; the bond strength necessary for irreversible adsorption and the absence of a clearly defined surface to which the antifreeze proteins may adsorb. This article deals with these apparent conflicts between the prevailing theory and the empirical observations. We first review the mechanism of thermal hysteresis with some modifications: we explain the hysteresis as a result of vapour pressure equilibrium between the ice surface and the ambient fluid fraction within the hysteresis gap due to a pressure build-up within the convex growth zones, and the ice growth as the result of an ice surface nucleation event at the hysteresis freezing point. We then go on to summarise the empirical data to show that the dependence of the hysteresis on the concentration of antifreeze proteins arises from an equilibrium exchange of antifreeze proteins between ice and solution at the melting point. This reversible association between antifreeze proteins and the ice is followed by an irreversible adsorption of the antifreeze proteins onto a newly formed crystal plane when the temperature is lowered below the melting point. The formation of the crystal plane is due to a solidification of the interfacial region, and the necessary bond strength is provided by the protein "freezing" to the surface. In essence: the antifreeze proteins are "melted off" the ice at the bulk melting point and "freeze" to the ice as the temperature is reduced to subfreezing temperatures. We explain the different hysteresis activities caused by different types of antifreeze proteins at equimolar concentrations as a consequence of their solubility features during the phase of reversible association between the proteins and the ice, i.e., at the melting point; a low water solubility results in a large fraction of the proteins being associated with the ice at the melting point. This leads to a greater density of irreversibly adsorbed antifreeze proteins at the ice surface when the temperature drops, and thus to a greater hysteresis activity. Reference is also made to observations on insect antifreeze proteins to emphasise the general validity of this approach.