The motion and stability of the ship under the marine environment is a full nonlinear dynamic system. Considering the nonlinear characteristics of ocean environmental loads on the ship and the natural nonlinear response characteristics of the ship motion, there are extensive studies and a series of theoretical and application results. The research methods of the nonlinear motion response and stability of ships based on the theory of nonlinear dynamics are summarized, thus revealing the nonlinear dynamic characteristics of the whole process of the ship motion instability, large-scale motion response, and even capsizing. It mainly focuses on the nonlinear analysis methods and main conclusions of the parametric rolling and surf-riding/broaching in regular and irregular waves. The combination of the nonlinear dynamics method and the seakeeping theory in the current study provides a new approach and method for the study of the ship motion and stability.