Vehicle vibration is a core topic in automotive dynamics because it affects ride comfort, road holding, structural durability, and driver health. A reliable vibration study normally requires two steps: selecting a suitable dynamic model and choosing an appropriate method to solve the governing vibration equations. This paper reviews common modeling approaches and solution methods used in vehicle vibration analysis, including quarter-car, half-car, full-vehicle, and extended cab-seat-driver models. Analytical solutions, transfer-function analysis, state-space formulation, numerical integration, MATLAB/Simulink simulation, frequency-domain analysis, and simulation-based optimization are discussed. The review shows that simple models remain useful for understanding basic vibration mechanisms, whereas full-vehicle and multi-degree-of-freedom models are more suitable for evaluating ride comfort, dynamic tire load, cab vibration, and seat vibration under practical operating conditions. Recent studies also show that optimization algorithms, including genetic algorithms and swarm-based methods, are increasingly used to improve suspension parameters and control performance, especially for electric vehicles.