Car-following behavior is the result of the interaction of various elements in the specific driver-vehicle-environment aggregation. Under the intelligent and connected condition, the information perception ability of vehicles has been significantly enhanced, and abundant information about the driver-vehicle-environment factors can be obtained and utilized to study car-following behavior. Therefore, it is necessary to comprehensively take into account the driver-vehicle-environment factors when modeling car-following behavior under intelligent and connected conditions. While there are a considerable number of achievements in research on car-following behavior, a car-following model with comprehensive consideration of driver-vehicle-environment factors is still absent. To address this gap, the literature with a focus on car-following behavior research with consideration of the driver, vehicle, or environment were reviewed, the contributions and limitations of the previous studies were analyzed, and the future exploration needs and prospects were discussed in this paper. The results can help understand car-following behavior and the traffic flow characteristics affected by various factors and provide a reference for the development of traffic flow theory towards smart transportation systems and intelligent and connected driving.