The use of metaheuristic, nature inspired algorithms for solving complex optimization problems with non-linearity and multimodality, has become a popular tool in the field of science and engineering. Presently, there has been much development of such tools, with academics creating new nature-inspired algorithms that could potentially be more efficient and effective. One such algorithm is the Flower Pollination Algorithm (FPA) developed by Xin-She Yang in 2012. This metaheuristic algorithm is modelled after the evolutionary process of flowering plants and has been useful in many fields of science and engineering, particularly in electrical power systems. With the rapid expansion of industries and population growth, engineers are faced with the arduous task of satisfying the growing electrical demand. To improve electrical power systems and reduce running costs, FPA and its variants have been implemented to determine optimal solutions to complex combinatorial optimization problems, with little computational effort, and has proven to be more effective than other popular metaheuristic algorithms, such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Owing to its balanced global and local search capabilities, and better convergence characteristics, numerous studies have been conducted to utilize FPA and its variants in real-world optimization problems. Thus, this paper aims to provide a comprehensive review of FPA and its variants to successfully determine optimal results to non-deterministic polynomial-time hard problems in electrical power systems and other fields of science. To accomplish this, an in- depth description of FPA and its parameters that influence its performance are discussed, including the various modifications and hybridizations of the algorithm. In addition, an in- depth review of applications using FPA and its variants in electrical power systems and other fields of science, is provided.