In this paper, the fictive temperature and relaxation dynamics theories of structural relaxation are introduced at first, and their establishment, development and research progress are discussed as well. The fictive temperature theory focuses on the thermal history of glass, and provides a thermodynamic criterion for determining the direction and velocity of relaxation process, while the relaxation dynamics theory places emphasis on glass transition phenomenon and aims to reveal microscopic mechanism and evolution process of structural relaxation. The thermal history, glass composition, impurities, defects, temperature, stress, moisture and size are key factors affecting the structural of inorganic glass. These factors are important issues of structure tailoring and safety analysis for manufacture and application of glass. Although the structural relaxation theories of glass have been rapidly developed, there are still many gaps in experimental studies, particularly for inorganic glass with complex composition, and the specific microscopic mechanism still needs further improvement. In addition, the structural relaxation of glass-ceramics and glass matrix composites has not received deserved attention. The breakthrough of such problems is expected to support long-term safety and reliability of inorganic glass under more stringent conditions.