The manufacturing industry is undergoing a profound transformation toward smart, digital, and flexible production systems under the Industry 4.0 framework. Within this paradigm, Digital Twin (DT) serves as a key enabler, bridging physical and digital domains to simulate, analyse, and optimise manufacturing operations. Concurrently, robotic systems, enhanced by smart sensor perception, Industrial Internet of Things connectivity, and adaptive control mechanisms, are increasingly deployed to handle complex and dynamic tasks. However, the evolving demands of the modern manufacturing industry require a high degree of flexibility and responsiveness, necessitating more intelligent solutions. The Robot Digital Twin (RDT) has emerged as a transformative approach, facilitating dynamic adaptation and continuous operational improvement. This review offers a comprehensive examination of the literature on RDT in manufacturing from both technology and application perspectives, aiming to provide insight for researchers and practitioners in Industry 4.0. The paper introduces a four-layer RDT system architecture and summarises how Industry 4.0 technologies, e.g., the Industrial Internet of Things, Cloud/Edge Computing, 5 G, Virtual Reality, Modelling and Simulation, and Artificial Intelligence, converge and influence the RDT system based on this architecture. Furthermore, the review covers domain-specific and system-level applications, such as assembly, machining, grasping, material handling, human-robot interaction, predictive maintenance, and additive manufacturing systems, with an analysis of their development status. Finally, the trends, practical challenges, and future research directions for RDT systems in manufacturing are summarised at different levels.