Smooth objects such as metals, optical mirrors, and silicon wafers generally have high reflectivity and extremely low emissivity, and extremely weak radiation from smooth objects will be completely submerged by the environmental radiation reflected from their surfaces. The infrared temperature measurement of smooth objects has always been a challenge in the field of infrared temperature measurement. Due to the continuously growing demand for non-contact temperature measurement of smooth objects in fields such as metal smelting, solar telescope thermal control, and semiconductor production, a large number of infrared temperature measurement methods for smooth objects have been proposed. First, this paper elaborates on the difficulties of the infrared temperature measurement of smooth objects and summarizes the many temperature measurement methods currently used for smooth objects into five categories. Then, the basic principles and technical routes of each temperature measurement method were summarized, and the advantages and disadvantages of each temperature measurement method were analyzed in detail. Finally, the possible development directions of temperature measurement for smooth objects were discussed.