Navigation is a fundamental component of modern information application systems, ranging from military, transportations, and logistic, to explorations. Traditional navigations are based on an absolute coordination system that provides a precise map of the physical world, the locations of the moving objects, and the optimized navigation routes. In recent years, many new emerging applications have presented new demands for navigation, e.g., underwater/underground navigations where no GPS or other localizations are available, an un-explored area with no maps, and task-oriented navigations without specific routes. The advances in IoT and AI enable us to design new navigation paradigms, embodied navigation that allows the moving object to interact with the physical world to obtain the local map, localize the objects, and optimize the navigation routes accordingly. We make a systematic and comprehensive review of research in embodied navigation, encompassing key aspects on perceptions, navigation and efficiency optimization. Beyond advancements in these areas, we also examine the emerging tasks enabled by embodied navigation which require flexible mobility in diverse and evolving environments. Moreover, we identify the challenges associated with deploying embodied navigation systems in the real world and extend them to substantial areas. We aim for this article to provide valuable insights into this rapidly developing field, fostering future research to close existing gaps and advance the development of general-purpose autonomous systems grounded in embodied navigation.