The rapid growth in the popularity of Augmented Reality (AR), Virtual Reality (VR), and Mixed Reality (MR) experiences have resulted in an exponential surge of three-dimensional data. Point clouds have emerged as a commonly employed representation for capturing and visualizing three-dimensional data in these environments. Consequently, there has been a substantial research effort dedicated to developing efficient compression algorithms for point cloud data. This Master's thesis aims to investigate the current state-of-the-art lossless point cloud geometry compression techniques, explore some of these techniques in more detail and then propose improvements and/or extensions to enhance them and provide directions for future work on this topic.