A fundamental task in robotics is to plan collision-free motions among a set of obstacles. Recently, learning-based motion-planning methods have shown significant advantages in solving different planning problems in high-dimensional spaces and complex environments. This article serves as a survey of various different learning-based methods that have been applied to robot motion-planning problems, including supervised, unsupervised learning, and reinforcement learning. These learning-based methods either rely on a human-crafted reward function for specific tasks or learn from successful planning experiences. The classical definition and learning-related definition of motion-planning problem are provided in this article. Different learning-based motion-planning algorithms are introduced, and the combination of classical motion-planning and learning techniques is discussed in detail.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.