In the study on phase transitions, heat capacity is one of important quantities since at almost all phase transitions heat capacity exhibits anomalous behavior. Phase transitions are characterized by two kinds of categories. One is a continuous transition where the order parameter becomes zero continuously at the transition temperature and the other is a discontinuous transition where the order parameter exhibits a jump at the transition temperature. The former includes so-called a second-order transition and the latter is called a first-order transition conventionally. Within framework of mean field approximation, it can be shown that heat capacity exhibits a jump at a continuous transition. However, in a much higher approximation or an exact solution heat capacity diverges at a continuous transition. In such a case, critical exponents are a useful parameter to know characteristics at a phase transition and scaling relations are also applicable to know self-consistency among critical exponents. It is pointed out that although critical amplitudes have been less noted so far, we have to pay attention to them. At a discontinuous transition, kinetics is important because heterogeneous structures result in it always. There are a lot of materials with microscopic heterogeneous structure which undergoes a state transformation. Dynamic heat capacity measurement is one of promising tools in such a field.