This chapter provides a systematic exposition of the most popular swarm intelligence optimization algorithms. Swarm intelligence refers to a class of computational methods inspired by the collective and self-organizing behaviors observed in biological groups, such as bird flocks, fish schools, bee colonies, and ant colonies. Although each individual in these systems follows relatively simple rules, intelligent global behavior can emerge through local interaction, cooperation, and information sharing. Because of this feature, swarm intelligence algorithms are especially suitable for solving complex optimization problems that are nonlinear, high-dimensional, uncertain, or difficult to address using traditional mathematical methods. The chapter focuses on two classical and representative algorithms: Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO). PSO imitates the social learning process of bird flocking. In this algorithm, each particle represents a possible solution and moves through the search space according to its own best experience and the best position found by the entire swarm. Owing to its simple structure, few control parameters, and fast convergence speed, PSO has been widely used in continuous optimization, function optimization, parameter tuning, and engineering design. ACO, in contrast, is inspired by the pheromone-based foraging behavior of ants. Artificial ants construct solutions step by step, while pheromone accumulation and evaporation guide the search toward promising paths. This positive feedback mechanism gives ACO clear advantages in combinatorial optimization problems, including path planning, scheduling, and routing. Overall, PSO and ACO complement each other in biological inspiration, search mechanism, and application domain. The chapter also discusses future research directions, such as dynamic adaptation, integration with deep learning, and large-scale parallel implementation.