Theoretical models regarding the thermodynamic aspects of contact angle hysteresis are reviewed. General thermodynamic considerations are briefly summarized in order to emphasize the local nature of the thermodynamic equilibrium condition regarding the contact angle. General considerations are also presented concerning the phenomenon of hysteresis, explaining the relationship between multiplicity of metastable equilibrium states, branching, and hysteresis. Models of various degrees of complexity are discussed, and their contribution to improving the understanding of contact angle hysteresis is presented. It is pointed out that in most models there is no consideration of the effect of varying the external constraint, such as the drop volume or the depth of a plate inside a liquid. It is stressed that calculating metastable contact angles for a system under a given constraint may not be sufficient. In order to understand contact angle hysteresis and use it to advantage for characterizing surfaces, the process of measuring hysteresis, i.e. the process of adjustment of the system to systematic variations in the external constraint, must be modelled. Possible effects of the drop volume on apparent contact angles are indicated for a simple model of heterogenous smooth surfaces.