Relative space is easier to be understood and used in navigation service by pedestrians. The basic characteristic of pedestrian navigation process is the relative space-based guidance by visual and spatial semantics within outdoor and indoor environment. It could be called relative pedestrian navigation. Current pedestrian navigation theory and technique are built upon the locating and modeling within the absolute space. It could not understand the difference of recognition ability of different pedestrians, especially on the relative visual and spatial semantics. The research community of pedestrian navigation doesn't have a relative space-based pedestrian navigation theory framework and technology, which makes the pedestrian services not friendly. This paper reviews the related studies on pedestrian navigation, such as the outdoor/indoor positioning, data collecting and organizing, route planning and guiding. Then, this paper concludes the potential research problems of pedestrian navigation, for example, the relative data collecting and modeling, relative semantic attracting, pedestrian navigation behavior sensing, multisensory interaction, and route choice and confirming mechanism. Finally, this paper introduces a three-stage divisions for the future pedestrian navigation studies.