Horizontal vibration in high-speed elevator car systems has been a serious problem affecting the riding feeling, and it may threaten the safety and stability of the elevator system. This review aims to provide a comprehensive overview of the causes of horizontal vibration, focusing on factors such as the car and guide system, aerodynamic characteristics, and the performance during starting and stopping processes. Subsequently, various models of high-speed elevator car systems were discussed in detail, taking into account structural excitations and aerodynamic effects. Finally, a thorough analysis of vibration suppression methods, addressing both passive and active controls, was presented. Compared to passive control, active damping control technology has been shown to offer a more flexible and efficient approach to vibration suppression by leveraging real-time feedback and dynamic adjustments of control forces. To enhance the suppression of horizontal vibration, further research into intelligent control strategies with self-learning capabilities, as well as the integration of intelligent materials, appears promising.