This article surveys one Internet mobility approach that is highlighted by the employment of an identifier namespace. This approach uses identifiers other than traditional IP addresses to name mobile hosts, contents, or other entities, and introduces a mapping function to locate the entities in the global scope. Although this approach has been adopted by many Internet mobility solutions and is also considered as a promising way to support mobility in the future Internet, there lacks a comprehensive review and analysis of this approach together with related solutions, especially the ones proposed in recent years. This article describes the emergence, evolution, and state of the art of the approach, and gives a classification, a review, and a comparison of typical solutions related to the approach. This article also presents discussions of open issues, challenges, and research trends on designing future Internet mobility solutions.