Moving in complex environments is an essential capability of intelligent mobile robots. Decades of research and engineering have been dedicated to developing sophisticated navigation systems to move mobile robots from one point to another. Despite their overall success, a recently emerging research thrust is devoted to developing machine learning techniques to address the same problem, based in large part on the success of deep learning. However, to date, there has not been much direct comparison between the classical and emerging paradigms to this problem. In this article, we survey recent works that apply machine learning for motion planning and control in mobile robot navigation, within the context of classical navigation systems. The surveyed works are classified into different categories, which delineate the relationship of the learning approaches to classical methods. Based on this classification, we identify common challenges and promising future directions.