Embodied intelligent human-following mobile robots are intelligent systems capable of recognizing, tracking, and coordinating their movement with human targets. They have gradually evolved from "functional tools" to "context-aware intelligent agents", marking a paradigm shift from "operating in the environment" to "understanding and acting in the environment through their bodies". Based on the embodied intelligence framework of "environment-body-intelligence", this paper systematically reviews the research progress and development trends of human-following mobile robots. First, it elaborates on the research background and objectives of embodied intelligence, discussing its scientific essence centered on environmental interaction, bodily experience, and emergent intelligence. Second, it outlines the technological evolution, typical application scenarios, and industrial trends. By conducting an in-depth analysis of key technologies such as multimodal sensors, computing and processing units, and motion execution mechanisms, the paper further explores the application requirements in typical scenarios such as warehousing and logistics, public transportation, and elderly care and rehabilitation. Next, it focuses on natural and efficient human-robot interaction mechanisms and collaborative strategies, which include human-robot interaction methods based on explicit commands, implicit states, physical contact, and social-emotional cues, as well as interaction strategies based on reinforcement learning, imitation learning, and transfer learning, all aimed at enhancing the robots′ operational fluency and social acceptance in social environments. Finally, the paper summarizes the main technical challenges in areas such as deep environmental cognition, dynamic bodily adaptation, and continuous intelligent evolution, and provides an outlook on future development directions.