Abstract: Driven by breakthroughs in next-generation artificial intelligence, embodied intelligence is rapidly advancing into industrial manufacturing. In flexible manufacturing, industrial embodied intelligence faces three core challenges: accurate process modeling and monitoring under limited perception, dynamic balancing between flexible adaptation and high-precision control, and the integration of general-purpose skills with specialized industrial operations. Accordingly, this survey reviews existing work from three viewpoints: Industrial Eye, Industrial Hand, and Industrial Brain. At the perception level (Industrial Eye), multimodal data fusion and real-time modeling in complex dynamic settings are examined. At the control level (Industrial Hand), flexible, adaptive, and precise manipulation for complex manufacturing processes is analyzed. At the decision level (Industrial Brain), intelligent optimization methods for process planning and line scheduling are summarized. By considering multi-level collaboration and interdisciplinary integration, this work reveals the key technological pathways of embodied intelligence for closed-loop optimization of perception-decision-execution in manufacturing systems. A three-stage evolution model for the development of embodied intelligence in flexible manufacturing scenarios, comprising cognition enhancement, skill transition, and system evolution, is proposed, and future development trends are examined, to offer both a theoretical framework and practical guidance for the interdisciplinary advancement of industrial embodied intelligence in the context of flexible manufacturing.