High entropy alloys (HEAs) contain 5 or more elements with atomic concentrations between 5-35%. A major motivation behind this definition is to design alloys with high values of ideal configurational entropy to improve the chances of producing single-phase solid solution alloys. The concepts of entropy and enthalpy are central to many HEA studies, but consideration of thermodynamic quantities is usually limited to ideal cases and other simplifications. Here we consider classical thermodynamic concepts as they apply to HEAs. We discuss the four terms that must be considered to understand phase competition, including the entropy and enthalpy of mixing for solid solutions, and formation entropies and enthalpies of ordered compounds. We show that configurational entropies of metallic solutions are rarely described by the Boltzmann equation, and we introduce other ‘surprises’ in thermodynamic terms for HEAs. We conclude that no single term consistently dominates the phase stability of complex, concentrated alloys.