Abstract: The capacity to construct a cognitive map is hypothesized to rest on two foundations: (1) dead reckoning (path integration); (2) the perception of the direction and distance of terrain features relative to the animal. A map may be constructed by combining these two sources of positional information, with the result that the positions of all terrain features are represented in the coordinate framework used for dead reckoning. When animals need to become reoriented in a mapped space, results from rats and human toddlers indicate that they focus exclusively on the shape of the perceived environment, ignoring non-geometric features such as surface colors. As a result, in a rectangular space, they are misoriented half the time even when the two ends of the space differ strikingly in their appearance. In searching for a hidden object after becoming reoriented, both kinds of subjects search on the basis of the object's mapped position in the space rather than on the basis of its relationship to a goal sign (e.g. a distinctive container or nearby marker), even though they have demonstrably noted the relationship between the goal and the goal sign. When choosing a multidestination foraging route, vervet monkeys look at least three destinations ahead, even though they are only capable of keeping a maximum of six destinations in mind at once.