Abstract:In recent years, research on Physarum polycephalum has become more popular after Nakagaki et al. (2000) performed their famous experiment showing that Physarum was able to find the shortest route through a maze. Subsequent researches have confirmed the ability of Physarum-inspired algorithms to solve a wide range of NP-hard problems. This review will through light on recent Physarum polycephalum biological aspects, mathematical models, and Physarum bio-inspired algorithms and their applications. Further, we have presented our new model to simulate Physarum in competition, where multiple Physarum interact with each other and with their environments. The bio-inspired Physarum in competition algorithms proved to have great potentials for future research.