Car-following theory is an important research direction in the field of intelligent transportation systems (ITS), it describes the one-by-one following process of vehicles on the same lane in traffic flow, and one of its important issues is congestion control. To explore the strategy for controlling traffic congestion, this paper introduces and analyzes some classic car-following models, and gives a systematic review of their developments. Moreover, in order to introduce the approach to analyze the stability, taking the full velocity difference (FVD) model for example, the local and asymptotic stability analysis is discussed, while the corresponding nonlinear analysis is also conducted. Then, some perspectives of the car-following model are given in the final.
