This paper summarizes the particle swarm optimization (PSO) related research to help readers have a comprehensive understanding. Firstly the paper presents the equations of motion and the calculation flow of PSO. Then we analyze the variations of particle swarm optimization and related parameters, includes basic algorithm, PSO with inertia weight and PSO with constriction factor. Thirdly we discuss the combination strategy with other intelligent methods (simulated annealing, genetic algorithm, ant colony optimization and immune operator) and point out the research about mathematics field of PSO is the convergence, which further to be discussed. The conclusion and prospect are in the end.