The car-following (CF) model is the core component for traffic simulations
and has been built-in in many production vehicles with Advanced Driving
Assistance Systems (ADAS). Research of CF behavior allows us to identify the
sources of different macro phenomena induced by the basic process of pairwise
vehicle interaction. The CF behavior and control model encompasses various
fields, such as traffic engineering, physics, cognitive science, machine
learning, and reinforcement learning. This paper provides a comprehensive
survey highlighting differences, complementarities, and overlaps among various
CF models according to their underlying logic and principles. We reviewed
representative algorithms, ranging from the theory-based kinematic models,
stimulus-response models, and cruise control models to data-driven Behavior
Cloning (BC) and Imitation Learning (IL) and outlined their strengths and
limitations. This review categorizes CF models that are conceptualized in
varying principles and summarize the vast literature with a holistic framework