  Car-following (CF) algorithms are crucial components of traffic simulations
and have been integrated into many production vehicles equipped with Advanced
Driving Assistance Systems (ADAS). Insights from the model of car-following
behavior help us understand the causes of various macro phenomena that arise
from interactions between pairs of vehicles. Car-following models encompass
multiple disciplines, including traffic engineering, physics, dynamic system
control, cognitive science, machine learning, and reinforcement learning. This
paper presents an extensive survey that highlights the differences,
complementarities, and overlaps among microscopic traffic flow and control
models based on their underlying principles and design logic. It reviews
representative algorithms, ranging from theory-based kinematic models,
Psycho-Physical Models, and Adaptive cruise control models to data-driven
algorithms like Reinforcement Learning (RL) and Imitation Learning (IL). The
manuscript discusses the strengths and limitations of these models and explores
their applications in different contexts. This review synthesizes existing
researches across different domains to fill knowledge gaps and offer guidance
for future research by identifying the latest trends in car following models
and their applications.
