Field investigations of geometric discontinuity properties in rock masses are increasingly using three-dimensional point cloud data. These point clouds sample the rock mass surface and are typically acquired by photogrammetry or LiDAR. The automatic segmentation and extraction of planar surfaces from point cloud data have attracted significant attention among researchers. This paper reviews the capabilities, merits, and limitations of different segmentation methods for discontinuity plane surface extraction and the specific challenges of processing point cloud data collected from rock faces. The segmentation and orientation results of a series of studies on two point cloud datasets of rock mass surfaces are critically discussed. A new set of ground truth orientations for one point cloud and some challenges faced while labeling a ground truth discontinuity plane are presented. Some suggestions to establish reliable and reproducible ground truth orientation results are presented. Two popular open-source software tools (CloudCompare and Discontinuity Set Extractor) for planar surface extraction are reviewed, and their capabilities and shortcomings are discussed. Acquisition of high-quality point cloud data and sharing it on a public repository establishes a basis for researchers to implement their methodologies and meaningfully compare their results to advance the knowledge in the field. Finally, some recommendations for future research and development are summarized.