This paper reviews the following behavior of human-driven vehicles (HDVs) and automated vehicles (AVs) under adverse weather conditions. As a basic framework for describing the following behavior, the car-following model is mainly used to simulate and predict the dynamic relationship between vehicles. Under adverse weather conditions (e.g., haze, snow, and rainfall), HDVs rely on the driver's experience and intuition, which involves greater uncertainty and risk. AVs can theoretically significantly improve driving safety and stability through a variety of sensors and intelligent algorithms, but under these conditions, the sensor performance may degrade, which in turn affects the driving safety of the vehicles. Studies have shown that adverse conditions significantly impact car-following behavior, and thus, the parameters of existing models need to be adapted to these environments. Future research will explore the relationship between HDVs, AVs, and fully-AVs to promote the development of smarter, safer, and more efficient intelligent transportation systems.