The rapid growth of 3D point cloud data, driven by applications in autonomous driving, robotics, and immersive environments, has led to criticals demand for efficient compression and quality assessment techniques. Unlike traditional 2D media, point clouds present unique challenges due to their irregular structure, high data volume, and complex attributes. This paper provides a comprehensive survey of recent advances in point cloud compression (PCC) and point cloud quality assessment (PCQA), emphasizing their significance for real-time and perceptually relevant applications. We analyze a wide range of handcrafted and learning-based PCC algorithms, along with objective PCQA metrics. By benchmarking representative methods on emerging datasets, we offer detailed comparisons and practical insights into their strengths and limitations. Despite notable progress, challenges such as enhancing visual fidelity, reducing latency, and supporting multimodal data remain. This survey outlines future directions, including hybrid compression frameworks and advanced feature extraction strategies, to enable more efficient, immersive, and intelligent 3D applications.