Topological/metric route following, also called teach and repeat (T&R), enables long‐range autonomous navigation even without globally consistent localization. In the teach pass, the robot is driven manually and builds up a topological/metric map of the environment, a graph of metric submaps connected by relative transformations. For repeating the route autonomously, the map only needs to be locally consistent; errors on the global level due to localization drift are irrelevant. This renders T&R ideal for applications in which a global positioning system may not be available, such as navigation through street canyons or forests in search and rescue, reconnaissance in underground structures, surveillance, or planetary exploration. We present a T&R system based on iterative closest point matching (ICP) using data from a spinning three‐dimensional (3D) laser scanner. Our algorithm is highly accurate, robust to dynamic scenes and extreme changes in the environment, and independent of ambient lighting. It enables autonomous navigation along a taught path in both structured and unstructured environments, including highly 3D terrain. Furthermore, our system is able to detect obstacles and avoid them by adapting its path using a local motion planner. It enables autonomous route following in nonstatic environments, which is not possible with classical T&R systems. We demonstrate our algorithm's performance in two long‐range driving experiments, one in a highly dynamic urban environment, the other in unstructured, rough, 3D terrain. In these experiments, our robot autonomously drove a distance of over 22 km in both day and night. We analyze the localization accuracy of our system and show that it is highly precise. Moreover, we compare our ICP‐based method to a state‐of‐the‐art stereo‐vision‐based technique and show that our approach has a greatly increased robustness to path deviations and is less dependent on environmental conditions.