Embodied intelligence stands as a strategic technology in the ongoing scientific and technological revolution, forming a frontier in global competition. The mobile manipulator robot system, with its exceptional mobility, planning, and execution capabilities, has become the preferred hardware carrier for embodied intelligence. Moreover, the mobile manipulator robot system, rooted in embodied intelligence, emerges as a pivotal platform capable of cross-domain functionality. Positioned at the forefront of a new era in information technology and artificial intelligence, this system is integral for future development. Addressing the strategic demand for embodied-intelligence-based mobile manipulator robot systems, this study presents an overview of the current developmental landscape. It delves into the challenges faced by this field, proposing key common technologies such as multimodal perception, world cognition, intelligent autonomous decision-making, and joint planning for movement and manipulation. Furthermore, the study offers recommendations for advancing the field, encompassing national policy support, breakthroughs in common technologies, interdisciplinary collaboration, talent cultivation, and construction of comprehensive verification platforms. These suggestions aim to facilitate the rapid progress of mobile manipulator robots in China amid the wave of embodied intelligence development.