Despite the fact that proteins are important molecules involved in almost all life phenomena, the principles of thermodynamic stability, the most fundamental topic of protein research, have not been elucidated. In this review, we first describe the thermodynamic properties of temperature-dependent denaturation (thermal and cold denaturation) and outline the generally accepted model of the denaturation mechanism (Kauzmann model). Then, the thermodynamic properties of pressure denaturation and the pressure dependence of the Gibbs energy of dissolution of hydrocarbons in water are presented. Comparison of these shows that the Kauzmann model cannot explain pressure denaturation of proteins. Since Gibbs free energy is a function of temperature and pressure, a correct denaturation model must be able to account for both temperature and pressure denaturation without contradiction. The temperature-pressure axial energy landscape of denaturation is essential for constructing a true model. Finally, we describe some recent theoretical and experimental studies on pressure denaturation mechanisms that have been very influential in this research field.