Digital twins, as precise digital representations of physical systems, have evolved from passive simulation tools into intelligent and autonomous entities through the integration of artificial intelligence technologies. This paper presents a unified four-stage framework that systematically characterizes AI integration across the digital twin lifecycle, spanning modeling, mirroring, intervention, and autonomous management. By synthesizing existing technologies and practices, we distill a unified four-stage framework that systematically characterizes how AI methodologies are embedded across the digital twin lifecycle: (1) modeling the physical twin through physics-based and physics-informed AI approaches, (2) mirroring the physical system into a digital twin with real-time synchronization, (3) intervening in the physical twin through predictive modeling, anomaly detection, and optimization strategies, and (4) achieving autonomous management through large language models, foundation models, and intelligent agents. We provide an in-depth analysis of the synergy between physics-based modeling and data-driven learning, highlighting the transition from traditional numerical solvers to physics-informed and foundation models for physical systems. Furthermore, we examine how generative AI technologies, including large language models and generative world models, transform digital twins into proactive and self-improving cognitive systems capable of reasoning, communication, and creative scenario generation. Through extensive review across eleven application domains such as healthcare, aerospace, smart manufacturing, robotics, and smart cities, we identify both universal challenges including scalability, explainability, and trustworthiness, as well as domain-specific requirements. This paper reveals how AI-driven digital twins are evolving toward more intelligent, interoperable, and ethically responsible ecosystems, highlighting key directions for future interdisciplinary research and development.