Autonomous robotic navigation in unstructured, complex environments requires the robot to robustly perceive its 3D surroundings, in order to intelligently plan around obstacles. Machine learning-based methods have significantly advanced the state of the art in object detection and segmentation, with both 2D images and 3D point clouds. These methods could enable robots to recognize obstacles in noisy, long-range sensor measurements, and to identify semantically meaningful areas in their surroundings. While these capabilities can potentially augment existing methods for autonomous path planning, challenges remaining in training machine learning perception models for robotics, and in incorporating the outputs of these models into the planning pipeline. In this dissertation, I present my work addressing challenges in 3D perception and planning for robotics. I first present Label Diffusion Lidar Segmentation (LDLS), a novel method for 3D scene segmentation that fuses information from a 3D lidar and an RGB camera to avoid any need for manual annotation of 3D point cloud data. I then present a method for self-supervised training of 3D stereo camera object detectors for robotics, using time series of data to annotate bounding boxes in noisy stereo point clouds. Finally, I present a path planner that uses uncertain object detections to enable safe navigation in obstacle-dense forest environments, reasoning about uncertainty to generate multiple hypothesis paths through the forest.