Ant Colony Optimization (ACO) is a metaheuristic approach for solving hard combinatorial optimization problems, inspired by the pheromone trail laying and following behavior of real ants. ACO uses artificial ants and pheromone trails to probabilistically construct solutions, adapting the trails based on search experience. The first ACO algorithm, Ant System (AS), was proposed for the Traveling Salesman Problem (TSP), though it initially did not compete with state-of-the-art algorithms. However, it stimulated further research on algorithmic variants and applications to various problems, including quadratic assignment, vehicle routing, scheduling, and network routing. ACO has been proposed as a common framework for existing applications and variants. ACO algorithms are used for both static and dynamic combinatorial optimization problems. Static problems have fixed topologies and costs, while dynamic problems involve changing topologies and costs. ACO algorithms are similar in high-level structure but differ in implementation details. Artificial ants use randomized heuristics based on pheromone trails and problem data, adapting trails during execution to reflect search experience. This chapter reviews traditional approximation approaches, defines ACO's application scope, describes its biological analogy, and discusses its applications and recent developments. ACO is an extension of traditional construction heuristics, with the key difference of pheromone trail adaptation. The chapter also covers the use of ACO in various problem types and discusses challenges and future research directions.Ant Colony Optimization (ACO) is a metaheuristic approach for solving hard combinatorial optimization problems, inspired by the pheromone trail laying and following behavior of real ants. ACO uses artificial ants and pheromone trails to probabilistically construct solutions, adapting the trails based on search experience. The first ACO algorithm, Ant System (AS), was proposed for the Traveling Salesman Problem (TSP), though it initially did not compete with state-of-the-art algorithms. However, it stimulated further research on algorithmic variants and applications to various problems, including quadratic assignment, vehicle routing, scheduling, and network routing. ACO has been proposed as a common framework for existing applications and variants. ACO algorithms are used for both static and dynamic combinatorial optimization problems. Static problems have fixed topologies and costs, while dynamic problems involve changing topologies and costs. ACO algorithms are similar in high-level structure but differ in implementation details. Artificial ants use randomized heuristics based on pheromone trails and problem data, adapting trails during execution to reflect search experience. This chapter reviews traditional approximation approaches, defines ACO's application scope, describes its biological analogy, and discusses its applications and recent developments. ACO is an extension of traditional construction heuristics, with the key difference of pheromone trail adaptation. The chapter also covers the use of ACO in various problem types and discusses challenges and future research directions.