Texture synthesis is of importance to computer vision and graphics. The technique has great potential in many applications, especially in image editing, computer animation, real-time rendering for large scale of scenes, realistic and non-photorealisitic rendering etc.. In this paper, a survey of traditional and contemporary texture synthesis methods is presented. Fast texture synthesis algorithm using PSO is an effective texture synthesis algorithm. Particle swarm optimization (PSO) is applied to improve the process of searching and matching in the texture synthesis by patch-based sampling, thus changing the throughout search method of the original algorithm and speeding up the process of synthesis without influencing the quality of the image. It is shown that high-quality texture can be synthesized in several seconds on a midlevel PC, and this algorithm works well for a wide variety of texture ranging from regular to stochastic. How the number of the particles and the iterations influence the speed of the synthesis is analyzed in detail.