In the last decade, the application of membrane-inspired evolutionary algorithms in real-life problems has attracted much attention due to their flexibility and parallelizability. Almost seven years have passed since the first membrane algorithms survey paper was published in 2014. Considering the importance and ongoing research on such algorithms and their applications in various disciplines, this paper presents a comprehensive review of the published literature and suggests future directions. This review aims to summarize and analyze membrane algorithms based on the used nature-inspired algorithm, membrane structure, membrane rules, and their merits and demerits. Furthermore, an extensive bibliography about their real-world applications is presented.