A wearable computer is a potential platform for map applications: it is mobile in nature, and is often equipped with a head-worn display capable of displaying maps of the surrounding area in graphical form. In this paper, we present a map application, called WalkMap, developed for wearable computers. We concentrate on the visual presentation of the map, and propose a visualisation method that is based on the perspective distortion of a regular two-dimensional bird''s-eye view map. We also describe the results of a field study, and compare the distorted view to a regular two-dimensional view. The results show that while a perspective visualisation is good for some navigational tasks, for some other tasks a regular map is preferred. We then continue by developing the visualisation further, and present a fully adjustable three-dimensional version of the map application, called WalkMap3D. WalkMap3D can display the map area in three dimensions, but is also capable of displaying both traditional two-dimensional and perspective map views.