Road surface roughness is the leading cause of vehicle oscillation. The suspension system is used to dampen these oscillations. The active suspension system equipped with a hydraulic actuator is more efficient than the passive one. Therefore, it is used to replace the passive suspension system. The article reviews and analyses models and control algorithms for active suspension systems. In this article, the author mentioned three dynamic models commonly used to simulate vehicle oscillations: a quarter-dynamic model, a half-dynamic model, and a fully dynamic model. Each hydraulic actuator can be considered a state variable in the dynamic model. Besides, the control algorithm for the suspension system is significant. Algorithms like PID (proportional–integral–derivative) and LQR (linear quadratic regulator) will fit the linear model. In contrast, the nonlinear model’s algorithms, such as SMC (sliding mode control), fuzzy, and ANN (artificial neural network), will perform better. Overall, vehicle oscillation can be significantly improved once an active suspension system is used. The contents analysed in this article will be the database for selecting control models and algorithms by other researchers in the future.