We introduce a dynamic technique for fast route planning in large road networks. For the first time, it is possible to handle the practically relevant scenarios that arise in present-day navigation systems: When an edge weight changes (e.g., due to a traffic jam), we can update the preprocessed information in 2–40 ms allowing subsequent fast queries in about one millisecond on average. When we want to perform only a single query, we can skip the comparatively expensive update step and directly perform a prudent query that automatically takes the changed situation into account. If the overall cost function changes (e.g., due to a different vehicle type), recomputing the preprocessed information takes typically less than two minutes. The foundation of our dynamic method is a new static approach that generalises and combines several previous speedup techniques. It has outstandingly low memory requirements of only a few bytes per node.