We introduce a new approach for exploration based on the concept of frontiers, regions on the boundary between open space and unexplored space. By moving to new frontiers, a mobile robot can extend its map into new territory until the entire environment has been explored. We describe a method for detecting frontiers in evidence grids and navigating to these frontiers. We also introduce a technique for minimizing specular reflections in evidence grids using laser-limited sonar. We have tested this approach with a real mobile robot, exploring real-world office environments cluttered with a variety of obstacles. An advantage of our approach is its ability to explore both large open spaces and narrow cluttered spaces, with walls and obstacles in arbitrary orientations.