During the past three decades, motion planning has emerged as a crucial and productive research area in robotics. In the mid-1980s, the most advanced planners were barely able to compute collision-free paths for objects crawling in planar workspaces. Today, planners efficiently deal with robots with many degrees of freedom in complex environments. Techniques also exist to generate quasi-optimal trajectories, coordinate multiple robots, deal with dynamic and kinematic constraints, and handle dynamic environments. This paper describes some of these achievements, presents new problems that have recently emerged, discusses applications likely to motivate future research, and finally gives expectations for the coming years. It stresses the fact that nonrobotics applications (e.g., graphic animation, surgical planning, computational biology) are growing in importance and are likely to shape future motion-planning research more than robotics itself.