The sixth-generation (6G) wireless communication system is expected to integrate communication, intelligence, sensing, positioning, control, and calculation to adapt to time critical, ultrareliable, and energy-saving data delivery, as well as accurate positioning of personnel and equipment, serving the Internet of Things (IoT). On the one hand, reconfigurable intelligent surface (RIS) can intelligently manipulate radio waves and is considered to be one of the candidate technologies for the 6G wireless communication. Hence, there are more and more surveys on RIS-assisted communications. On the other hand, the potential of RIS in positioning has attracted growing attention, and articles on RIS-assisted positioning have been blown out. Therefore, it is time to review this literature to understand the potential of RIS positioning, research status, and point out the direction for future research. This article first explains the working principle and channel model of RIS and summarizes some characteristics of RIS suitable for positioning. Then, we give a concise review and classification of existing RIS positioning research. Finally, we put forward our views on the future research challenges and attractive directions for RIS-aided wireless positioning technology.