Knowledge of the thermal diffusivity D and thermal conductivity kappa of olivine and its high-pressure polymorphs, wadsleyite and ringwoodite, is crucial to understand the heat transfer efficiency and thermal structure of Earth's mantle. In the last few decades, great progress has been made in measurement techniques and experimental results seeking to determine the thermophysical properties of geomaterials. The aim of this paper is to provide a systematic overview of the current knowledge of the thermal transport properties of olivine and its high-pressure polymorphs, their dependence on factors, such as pressure, temperature, and composition, and physical models to describe their variations. Some related geoscience applications and perspectives for the future are also suggested.