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Digital Twins (DTs) have extended beyond the original concept of a static digital model, to a dynamic, data-driven, and increasingly intelligent cyber-physical structure, which underlies modern Industry 4.0 systems. The paper gives a comprehensive and integrative conceptualization of DTs, Cognitive Digital Twins (CDTs), and agentic AI-enhanced DTs through an organized narrative literature review which synthesizes the foundational definitions, the theoretical differences between DTs and Cyber-Physical Systems (CPS), and the evolution of Digital Models and Digital Shadows to fully synchronous, two-way DTs. The research synthesizes the major architectural models, such as layered, multi-dimensional, cognitive and agentic models, and discusses the facilitating technologies that enable real-time synchronization, semantic reasoning, and autonomous decision-making. The state-of-the-art analysis indicates that the key research trends include ecosystem-based DTs, AI-driven analytics, semantic enrichment, and the development of LLM-enabled agentic DTs that are able to plan and coordinate actions in a goal-oriented manner. The paper also compares industrial and open-source DT platforms, outlines the present-day limitations in semantic interoperability, cognitive integration, and autonomy, and demonstrates real-world applications in manufacturing, healthcare, smart cities, and energy systems. The discussion proposes future research directions such as standardized cognitive layers, safe LLM grounding, multi-DT coordination, and governance frameworks of autonomous DT ecosystems. Overall, the paper contributes a unified conceptual model and a holistic synthesis that connects theory, architecture, technology, and application, providing a foundation for advancing the next generation of intelligent Digital Twin systems.