Connect-4, a solved two-player perfect-information game, offers a compact benchmark for artificial intelligence research due to its strategic depth and structural regularities, including board symmetries. This review presents a taxonomy-driven synthesis of Connect-4 AI research, encompassing game-theoretical foundations, classical search algorithms, reinforcement learning methods, explainable AI, and formal verification approaches. Analysis of search-, learning-, and hybrid-based methods reveals three dominant patterns: (i) classical search techniques prioritize determinism and efficiency but face scalability limits; (ii) reinforcement learning and neural approaches improve adaptability at the cost of interpretability and computational resources; and (iii) explainable and formally verified frameworks enhance transparency and reliability while imposing additional performance constraints. Recent advances in Connect-4 AI are driven less by raw performance gains than by strategic integration of efficiency, adaptability, interpretability, and robustness. Structuring the literature through a multidimensional taxonomy clarifies conceptual relationships, highlights underexplored research intersections, and points to emerging trends, including hybrid search–learning systems and explainable game intelligence. Overall, Connect-4 serves as a concise experimental domain for investigating fundamental challenges in game-playing AI, system design, and human–AI interaction.