A comprehensive review of firefly algorithms is presented, highlighting their application in various optimization and engineering problems. The firefly algorithm (FA), inspired by the flashing behavior of fireflies, is a stochastic, nature-inspired, meta-heuristic algorithm used for solving complex optimization problems. It is characterized by its ability to balance exploration and exploitation, and it has been successfully applied to continuous, combinatorial, constrained, multi-objective, dynamic, and noisy optimization problems. The algorithm is also applicable to classification tasks in machine learning, data mining, and neural networks, as well as various engineering applications such as image processing, industrial optimization, wireless sensor networks, antenna design, business optimization, robotics, semantic web, chemistry, and civil engineering. The FA is based on the physical formula of light intensity, which decreases with the square of the distance. The algorithm's performance is influenced by parameters such as the randomization parameter α, the attractiveness β, and the absorption coefficient γ. The algorithm has been modified and hybridized with other optimization algorithms, machine learning techniques, and heuristics to improve its efficiency and adaptability. These modifications include the use of binary representations, Gaussian and Lévy flight strategies, chaos-based approaches, and hybridization with other algorithms such as genetic algorithms, differential evolution, and ant colony optimization. The paper discusses the biological foundations of the firefly algorithm, its structure, and characteristics. It also reviews the classification and analysis of firefly algorithms, including classical, modified, and hybrid versions. The applications of the firefly algorithm are categorized into continuous, combinatorial, constrained, multi-objective, dynamic, and noisy optimization, as well as classification problems and engineering applications. The review concludes that the firefly algorithm is a powerful and efficient tool for solving a wide range of optimization and engineering problems.A comprehensive review of firefly algorithms is presented, highlighting their application in various optimization and engineering problems. The firefly algorithm (FA), inspired by the flashing behavior of fireflies, is a stochastic, nature-inspired, meta-heuristic algorithm used for solving complex optimization problems. It is characterized by its ability to balance exploration and exploitation, and it has been successfully applied to continuous, combinatorial, constrained, multi-objective, dynamic, and noisy optimization problems. The algorithm is also applicable to classification tasks in machine learning, data mining, and neural networks, as well as various engineering applications such as image processing, industrial optimization, wireless sensor networks, antenna design, business optimization, robotics, semantic web, chemistry, and civil engineering. The FA is based on the physical formula of light intensity, which decreases with the square of the distance. The algorithm's performance is influenced by parameters such as the randomization parameter α, the attractiveness β, and the absorption coefficient γ. The algorithm has been modified and hybridized with other optimization algorithms, machine learning techniques, and heuristics to improve its efficiency and adaptability. These modifications include the use of binary representations, Gaussian and Lévy flight strategies, chaos-based approaches, and hybridization with other algorithms such as genetic algorithms, differential evolution, and ant colony optimization. The paper discusses the biological foundations of the firefly algorithm, its structure, and characteristics. It also reviews the classification and analysis of firefly algorithms, including classical, modified, and hybrid versions. The applications of the firefly algorithm are categorized into continuous, combinatorial, constrained, multi-objective, dynamic, and noisy optimization, as well as classification problems and engineering applications. The review concludes that the firefly algorithm is a powerful and efficient tool for solving a wide range of optimization and engineering problems.