Abstract: The generalized Hamiltonian system (GHS), defined directly by thegeneralized Poisson bracket, is a generalization of the traditional Hamiltoniansystem defined on (even dim.) symplectic manifold. The GHS can describe moregeneral dynamical systems including odd- and ∞-dimensional systems, hence thestudy on this type of systems will bc very important in theory and applications.In this paper, we give a review on the researches of generalized Hamiltoniansystems in China and abroad.