This review explores the collective behaviors of ant colonies to understand how decentralized, self-organized systems achieve complex coordination, adaptability, and stability, which makes ants one of the most successful and widespread species globally. It highlights three key features of collective behavior behind the success of ant species that contribute to colony effectiveness: (1) individual heterogeneity, where varied traits support specialized roles within the colony; (2) task-oriented cooperation among individuals, allowing them to accomplish objectives beyond individual capacity; and (3) distributed decision-making and information flow, which optimize responses and resilience under changing conditions. Classic examples, including task allocation, cooperative transport, and quorum-based decision-making, illustrate how these three features enable ants to adapt flexibly to their environments. This review emphasizes the role of mathematical modeling as a research framework, providing precise insights for these complex behaviors by quantitative analysis. Quantifying and modeling ant colony behaviors is of great significance for translating natural intelligence into scalable, adaptable solutions to human social problems.