Mammalian grid cells discharge when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. In this talk, I will show how animals can use this code by reading out the grid-cell population activity across multiple spatial scales. The theory explains key experimental results (grid-field alignment, modularity, grid-scale ratio), makes testable predictions for future physiological and behavioral studies (specific changes in foraging when particular parts of the system are silenced), and provides a mathematical foundation for the concept of a "neural metric" for space. For goal-directed navigation, the proposed allocentric grid-cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. These results show that the grid-cell code provides a powerful and highly flexible neural substrate for spatial cognition.