Ant Colony Optimization (ACO) is a metaheuristic approach inspired by the pheromone trail-laying and following behavior of real ants. The pheromone trails serve as a distributed, numerical communication medium that ants use to probabilistically construct solutions and adapt during the algorithm's execution. The first ACO algorithm, Ant System (AS), was proposed for the Traveling Salesman Problem (TSP) but later evolved into more efficient variants and was applied to a wide range of problems, including quadratic assignment, vehicle routing, and scheduling. ACO algorithms are categorized into static and dynamic combinatorial optimization problems, with the former having fixed topology and costs, and the latter having changing topology and costs. The ants in ACO implement a randomized construction heuristic, making probabilistic decisions based on pheromone trails and heuristic information. The chapter outlines the historical development of ACO, its application to various problems, and discusses recent advancements and future research directions. Traditional approximation approaches, such as construction algorithms and local search algorithms, are also briefly reviewed, highlighting their differences and importance in solving hard combinatorial optimization problems.Ant Colony Optimization (ACO) is a metaheuristic approach inspired by the pheromone trail-laying and following behavior of real ants. The pheromone trails serve as a distributed, numerical communication medium that ants use to probabilistically construct solutions and adapt during the algorithm's execution. The first ACO algorithm, Ant System (AS), was proposed for the Traveling Salesman Problem (TSP) but later evolved into more efficient variants and was applied to a wide range of problems, including quadratic assignment, vehicle routing, and scheduling. ACO algorithms are categorized into static and dynamic combinatorial optimization problems, with the former having fixed topology and costs, and the latter having changing topology and costs. The ants in ACO implement a randomized construction heuristic, making probabilistic decisions based on pheromone trails and heuristic information. The chapter outlines the historical development of ACO, its application to various problems, and discusses recent advancements and future research directions. Traditional approximation approaches, such as construction algorithms and local search algorithms, are also briefly reviewed, highlighting their differences and importance in solving hard combinatorial optimization problems.