AbstractIn recent years, research on Physarum polycephalum has become more popular after Nakagaki (AIR 407: 6803-470, 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 real-world applications. In contrast to previous reviews that either focus on biological aspects or bio-inspired applications, here we present a comprehensive review that highlights recent Physarum polycephalum biological aspects, mathematical models, and Physarum bio-inspired algorithms and their applications. The novelty of this review stems from our exploration of Physarum intelligent behaviour in competition settings. 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.