In this chapter we describe popular ways to represent the environment of a mobile robot. For indoor environments, which are often stored using two-dimensional representations, we discuss occupancy grids, line maps, topologicalmaps, and landmark-based representations. Each of these techniques has its own advantages and disadvantages. Whilst occupancy grid maps allow for quick access and can efficiently be updated, line maps are more compact. Also landmark-basedmaps can efficiently be updated and maintained, however, they do not readily support navigation tasks such as path planning like topological representations do.

Additionally, we discuss approaches suited for outdoor terrain modeling. In outdoor environments, the flat-surface assumption underling many mapping techniques for indoor environments is no longer valid. A very popular approach in this context are elevation and variants maps, which store the surface of the terrain over a regularly spaced grid. Alternatives to such maps are point clouds, meshes, or three-dimensional grids, which provide a greater flexibility but have higher storage demands.