This paper surveys lateral and longitudinal vehicle control algorithms in automated highway systems. In the lateral control, an onboard sensing system detects or captures a reference on a roadway indicating the path of an automated vehicle, and PID control and state variable feedback control based on the modern control theory with deviation from a planned path are mainly used to drive the vehicle along the path. In the longitudinal control, an inter-vehicle gap and relative speed to a preceding vehicle are measured, and feedback control with state variables including deviations in the gap, relative speed, and relative acceleration, some of which are obtained by the transmission over inter-vehicle communication rather the measurement, is used to maintain a predetermined gap in a platoon. Lateral and longitudinal vehicle control algorithms are explained with references to some systems developed since 1960’s.