dThe assumptions and results associated with the McCabe-Thiele method of distillation column analysis are brought together within a rigorous analytical framework. Within this framework, the assumption that the saturated liquid and vapor enthalpy curves are parallel lines, apart from adiabatic and isobaric operation of the distillation column, is shown to be sufficient to derive all the major results of the McCabe-Thiele method including the constant molar overflow condition. Then, using a rigorous thermodynamic analysis, a comprehensive set of conditions sufficient for the enthalpy curves to be parallel lines are obtained. Some common systems for which these assumptions hold are discussed. Finally, the conditions under which McCabe-Thiele-like methods occur in other separation processes are outlined, with pointers to a unified picture of separation processes.