Thermal conductivity is one of the most fundamental properties of solid materials. The thermal conductivity of ideal crystal materials has been widely studied over the past hundreds years. On the contrary, for amorphous materials that have valuable applications in flexible electronics, wearable electrics, artificial intelligence chips, thermal protection, advanced detectors, thermoelectrics, and other fields, their thermal properties are relatively rarely reported. Moreover, recent research indicates that the thermal conductivity of amorphous materials is quite different from that of ideal crystal materials. In this article, the authors systematically review the fundamental physical aspects of thermal conductivity in amorphous materials. They discuss the method to distinguish the different heat carriers (propagons, diffusons, and locons) and the relative contribution from them to thermal conductivity. In addition, various influencing factors, such as size, temperature, and interfaces, are addressed, and a series of interesting anomalies are presented. Finally, the authors discuss a number of open problems on thermal conductivity of amorphous materials and a brief summary is provided. A systematic review of the fundamental physical aspects of thermal conductivity in amorphous materials, which have valuable applications in flexible electronics, artificial intelligence chips, thermal protection, and thermoelectrics, is presented. The contributions from different heat carriers, including propagons, diffusons, and locons, are comprehensively discussed. Various influencing factors are addressed, and a series of interesting anomalies are presented.