Some embodiments of the invention provide a navigation application that allows a user to peek ahead or behind during a turn-by-turn navigation presentation that the application provides while tracking a device (e.g., a mobile device, a vehicle, etc.) traversal of a physical route. As the device traverses along the physical route, the navigation application generates a navigation presentation that shows a representation of the device on a map traversing along a virtual route that represents the physical route on the map. While providing the navigation presentation, the navigation application can receive user input to look ahead or behind along the virtual route. Based on the user input, the navigation application moves the navigation presentation to show locations on the virtual route that are ahead or behind the displayed current location of the device on the virtual route. This movement can cause the device representation to no longer be visible in the navigation presentation. Also, the virtual route often includes several turns, and the peek ahead or behind movement of the navigation presentation passes the presentation through one or more of these turns. In some embodiments, the map can be defined presented as a two-dimensional (2D) or a three-dimensional (3D) scene.