Specific heat is one of the most fundamental thermodynamic properties of substances. By measuring and studying low temperature specific heat, we can not only calculate the corresponding thermodynamic functions (e.g., entropy, enthalpy and Gibbs free energy), but also obtain the information of materials related to their physical properties, energetics, molecular structures and phase transitions. Therefore, specific heat measurement could establish an important basis for the research and exploration of relevant thermodynamic issues. Adiabatic, alternating-current and relaxation calorimetry are commonly used methods for the low temperature specific heat measurement. Relaxation calorimetry has become the most popular low temperature specific heat measurement method due to its small sample amounts, extremely low temperature measurement regions, high measurement accuracy, simple operation procedure and available commercial instruments. In this review, we presented a brief introduction about the measurement concept and development process of relaxation calorimetry, and reviewed the recent work on the specific heat measurement technique improvement and the related thermodynamic property investigation on materials using this calorimetric method.