Industrialized buildings, characterized by off-site manufacturing and on-site installation, offer notable improvements in efficiency, cost-effectiveness, and material use. This transition from traditional construction methods not only accelerates building processes but also enhances working efficiencies globally. Despite its widespread adoption, the performance of industrialized building manufacturing (IBM) can still be optimized, particularly in enhancing time efficiency and reducing costs. This paper explores the integration of Artificial Intelligence (AI) and robotics at IBM to improve efficiency, cost-effectiveness, and material use in off-site assembly. Through a narrative literature review, this study systematically categorizes AI-based Robots (AIRs) applications into four critical stages-Cognition, Communication, Control, and Collaboration and Coordination, and then investigates their application in the factory assembly process for industrialized buildings, which is structured into distinct stages: component preparation, sub-assembly, main assembly, finishing tasks, and quality control. Each stage, from positioning components to the integration of larger modules and subsequent quality inspection, often involves robots or human-robot collaboration to enhance precision and efficiency. By examining research from 2014 to 2024, the review highlights the significant improvements AI-based robots have introduced to the construction sector, identifies existing challenges, and outlines future research directions. This comprehensive analysis aims to establish more efficient, precise, and tailored construction processes, paving the way for advanced IBM.