Integration of digital twins and physical AI in cyber-physical systems

• Synthesizes DT technologies across manufacturing, agriculture, automotive, energy, and healthcare, identifying shared principles and domain-specific innovations. • First review centered on DT-physical (embodied) AI integration, highlighting sim-to-real transfer and adaptive robotic control in cyber-physical systems. • Classifies DTs (data-driven, model-based, hybrid) while emphasizing their practical continuum and prevalence of hybrid approaches. • Integrates analysis of interdependent DT deployment issues for deeper insights into barriers and research gaps. • Positions DTs as core enablers of intelligent, adaptive systems in Industry 4.0/5.0 through architectures, standards, and applications. Digital twins (DTs) have become a transformative technology for modern cyber-physical systems, enabling real-time synchronization between physical assets with their digital counterparts. By integrating data acquisition, advanced simulation, and artificial intelligence (AI), DTs offer predictive, diagnostic, and prescriptive insights that improve performance across various domains. This review examines the current state of DT research and implementation, with a focus on their integration with physical AI systems. We categorize different types of DTs, and analyze their architectures, standards, and interoperability frameworks that facilitate scalable deployment. Then, we explore applications in key industrial sectors such as manufacturing, agriculture, automotive, and energy, highlighting benefits in simulation, predictive maintenance, and real-time optimization. Finally, we address ongoing challenges related to data integration, model validation, scalability, and cybersecurity, while identifying opportunities for future research. Particularly for hybrid DTs in physical AI, we examine interdependent challenges including scalable verification, validation, and uncertainty quantification for real-time reliability; automated decision-making amid data-physics uncertainties; interoperability and ethical barriers to adoption; and robust taxonomies for societal-scale systems. The study indicates the critical role of DT as foundational technology for intelligent, connected, and adaptive industrial systems.