Incremental heuristic search methods use heuristics to focus their search and reuse information from previous searches to find solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. In this paper, we apply Lifelong Planning A* to robot navigation in unknown terrain, including goal-directed navigation in unknown terrain and mapping of unknown terrain. The resulting D* Lite algorithm is easy to understand and analyze. It implements the same behavior as Stentz' Focussed Dynamic A* but is algorithmically different. We prove properties about D* Lite and demonstrate experimentally the advantages of combining incremental and heuristic search for the applications studied. We believe that these results provide a strong foundation for further research on fast replanning methods in artificial intelligence and robotics.