As the voltage level of the grid continuously rises, more and more new insulating materials with better performance are put into use. Nevertheless, air gaps often appear in insulating materials due to poor material quality, structural design flaws, etc. High-field-strength air gaps will produce partial discharge or even breakdown, resulting in electrical equipment failure. In addition, during operation, organic insulating materials are simultaneously exposed to high temperatures, mechanical stress, electrical stress, and moisture. Consequently, aging is inevitable. The aging of insulation materials is the root cause of the reduced insulation properties of the degradation of the insulation properties of electrical equipment in long-term operation. In order to improve the safety performance of power equipment and assure the safety of power grids, the detection and identification of internal structural defects and aging states of insulating materials have always been hot issues in related fields. However, structural defects inside the insulation materials used in power equipment, which are tiny (microns to millimeters), are exceedingly challenging to detect. While there are various destructive methods for detecting the aging status, non-destructive in-line inspection methods are still less commonly reported. In recent years, some scholars have begun to try to use terahertz spectroscopy to detect insulating materials. Numerous scholars have discovered that terahertz spectroscopy can not only detect structural defects inside insulating materials but can also detect nondestructive testing on the degree of material aging and even the type of material, which has excellent engineering value and promotion prospects. In order to help relevant researchers understand the application of this emerging technology in the field of insulating materials, this paper reviews the basic principles of terahertz detection and its applications in air gap detection, moisture detection, and aging analysis of insulating materials. Existing problems and future development directions are discussed.