This article presents an overview of the recent standardization activities for point cloud compression (PCC). A point cloud is a 3D data representation used in diverse applications associated with immersive media including virtual/augmented reality, immersive telepresence, autonomous driving and cultural heritage archival. The international standard body for media compression, also known as the Motion Picture Experts Group (MPEG), is planning to release in 2020 two PCC standard specifications: video-based PCC (V-CC) and geometry-based PCC (G-PCC). V-PCC and G-PCC will be part of the ISO/IEC 23090 series on the coded representation of immersive media content. In this paper, we provide a detailed description of both codec algorithms and their coding performances. Moreover, we will also discuss certain unique aspects of point cloud compression.