The problem of creating machines capable of intelligent thought and decision-making similar to human cognition has long plagued the science of artificial intelligence. One promising method in this field is the Adaptive Control of Thought-Rational cognitive architecture, which attempts to simulate the fundamental cognitive mechanisms that underlie human behavior and problem-solving. This survey presents a detailed analysis of the theoretical and historical development of ACT-R. It is a comprehensive analysis of ACT-R, considering its basic concepts, key components, and potential applications in AI system design. For researchers and practitioners interested in exploring or extending the capabilities of ACT-R, this survey is a highly valuable resource. Simulating human thought processes is the ACT-R; it is a foundational cognitive architecture that bridges the gap between artificial intelligence and cognitive science. This review comprehensively synthesizes insights across the studies that tell a lot about ACT-R theory and contributions toward modeling human cognition.