Design automation is a core technology in industrial design software and an important branch of knowledge-worker automation. For example, electronic design automation (EDA) has played an important role in both academia and industry. Design automation for intelligent robots refers to the construction of unified modular graph models for the morphologies (body), controllers (brain), and vision systems (eye) of intelligent robots under digital twin architectures, which effectively supports the automation of the morphology, controller, and vision system design processes of intelligent robots by taking advantage of the powerful capabilities of genetic programming, evolutionary computation, deep learning, reinforcement learning, and causal reasoning in model representation, optimization, perception, decision making, and reasoning. Compared with traditional design methods, MOdular DEsigN Automation (MODENA) methods can significantly improve the design efficiency and performance of robots, effectively avoiding the repetitive trial-and-error processes of traditional design methods, and promoting automatic discovery of innovative designs. Thus, it is of considerable research significance to study MODENA methods for intelligent robots. To this end, this paper provides a systematic and comprehensive overview of applying MODENA in intelligent robots, analyzes the current problems and challenges in the field, and provides an outlook for future research. First, the design automation for the robot morphologies and controllers is reviewed, individually, with automated design of control strategies for swarm robots also discussed, which has emerged as a prominent research focus recently. Next, the integrated design automation of both the morphologies and controllers for robotic systems is presented. Then, the design automation of the vision systems of intelligent robots is summarized when vision systems have become one of the most important modules for intelligent robotic systems. Then, the future research trends of integrated “Body-Brain-Eye” design automation for intelligent robots are discussed. Finally, the common key technologies, research challenges and opportunities in MODENA for intelligent robots are summarized.