The particle swarm optimization (PSO) algorithm is a new type global searching method, which mostly focus on the continuous variables and little on discrete variables. The discrete forms and discretized methods have received more attention in recent years. This paper introduces the basic principles and mechanisms of PSO algorithm firstly, then points out the process of PSO algorithm and depict the operation rules of discrete PSO algorithm. Various improvements and applications of discrete PSO algorithms are reviewed. The mechanisms and characteristics of two different discretized strategies are presented. Some development trends and future research directions about discrete PSO are proposed.