This project reviews various path following and trajectory tracking methods to track a reference point on the path which represents the rate of change of parameter of the trajectory. The aim is to minimize the euclidean distance between the vehicle and above mentioned reference point. Moreover the other concerns would be to reduce the cross-track error and the heading error. The methods like pure pursuit and its variations are described. The Stanley method of path following and other trajectory tracking methods like control Lyapunov Based Design and its modifications are analyzed. This paper has also looked into MPC(Model Predictive Control) and its variations for applying it to trajectory tracking. Simulations were done on kinematic model of car in MATLAB to find the best method to achieve the objective.