Abstract: This paper is a summary of the applications of symplectic theories and symplectic algorithms to Hamiltonian mechanics and the research progress Hamiltonian formulation for nonlinear water waves.The advanages and limitations of Hamiltonian variational principle and approaches for nonlineax water waves are discussed.In addition, it includes also discussions on the Hamiltonian formalism, symmetry and conseryation laws of KdV equation and BBM equation and comments on the problems concerned.