Car-following is the most common driving task. It refers to a process where the following vehicle (FV) tries to keep a safe distance between itself and the lead vehicle (LV) by adjusting its acceleration in response to the actions of the vehicle ahead. The corresponding car-following models are functions that determine FV’s future accelerations based on current (and historical) driving situations. Car-following models are the cornerstone for microscopic traffic simulation and intelligent vehicle development. One major motivation of car-following models is to replicate human drivers' longitudinal driving trajectories. In this seminar, I will first talk about how to calibrate, evaluate, and cross-compare classical car-following models using large-scale real-world naturalistic driving data. To model the long-term dependency of future actions on historical driving situations, I will also introduce a long-sequence car-following trajectory prediction model based on the attention-based Transformer model. Then, I will talk about two autonomous car-following algorithms developed by deep reinforcement learning: one performs human-like car following with significantly higher accuracy than traditional car-following models, and the other demonstrates a better capability of safe, efficient, and comfortable driving than human drivers. I will also give a brief mention about other car-following related studies including comparing driving behavior across the US and China, the impact of forward collision warning systems on car-following behavior, and visual car-following models.