Navigating, and studying spatial navigation, is difficult enough in two dimensions when maps and terrains are flat. Here we consider the capacity for human spatial navigation on sloped terrains, and how sloping terrain is depicted in 2D map representations, called topographic maps. First, we discuss research on how simple slopes are encoded and used for reorientation, and to learn spatial configurations. Next, we describe how slope is represented in topographic maps, and present an assessment (the Topographic Map Assessment), which can be administered to measure topographic map comprehension. Finally, weThe Lay of the Land 2 describe several approaches our lab has taken with the aim of improving topographic map comprehension, including gesture and analogy. The current research reveals a rich and complex picture of topographic map understanding, which likely involves perceptual expertise, strong spatial skills, and inferential logic.There are many ways to navigate the spatial world. In the past decade, we have come to rely on technology to find our destinations, using computers and smart phones to provide step-by-step instructions on the best route, display an overall map, or tell us which way is north (if we choose to ask that question). But humans did not evolve in the technological world, although they eventually created it. Our ancestors used many cues for wayfinding. Some of these systems were part of a common evolutionary heritage, shared with other mammals and also with birds, insects and even with reptiles and amphibians, as would be expected given the importance of successful navigation for survival. But humans' abilities for abstract and symbolic reasoning also supported our species in the invention of complex and culturally communicated systems (Gladwin 1970;Hutchins 1995;Huth 2013), and increasingly, technological tools. Thus, for humans, understanding navigation entails both understanding shared cross-species capacities for navigation, and the uniquely human symbolic additions that augment those capacities.Modern cross-species research on navigation has generally concentrated on two navigation systems, often called the egocentric and allocentric systems (for reviews, see Jacobs & Menzel 2014;Wiener et al. 2011). These systems are distinct, but they can combine and supplement each other in various ways (e.g., Zhao & Warren 2015). Egocentric systems involve our bodily senses and body-centered encoding of spatial location, e.g., the window is behind me. Egocentric coding is useful for wayfinding only if it is updated by information about our movement through space, both in terms of direction (e.g., we know that the window that was behind us is now to our left, after we turn 90 degrees), and distance (e.g., we know that the window is now much further behind us after we walk 100 paces forward). When egocentric systems are updated in this way, they are often called inertial navigation systems, or dead reckoning. Allocentric coding does not depend on the body, but rather uses external landmarks, s...