Light Detection and Ranging (LiDAR) technology plays a pivotal role in numerous fields, including autonomous navigation, high-precision geospatial mapping, environmental monitoring, and infrastructure assessment. By generating accurate three-dimensional point clouds, LiDAR systems enable advanced spatial analysis, yet the massive volume and density of the acquired data present major challenges for storage, transmission, and real-time processing. With increasing sensor resolution and acquisition rates, the demand for efficient compression techniques has become more critical than ever. This paper presents a comprehensive survey of LiDAR data compression methods, systematically classifying them into lossless approaches, which preserve complete data fidelity, and lossy approaches, which achieve higher compression ratios by permitting controlled data degradation. Traditional methods, such as entropy encoding, predictive coding, and transform-based techniques, are discussed alongside modern deep learning-based models that exploit neural networks, particularly autoencoders, to learn compact and efficient data representations. A detailed comparison of methods is provided, analyzing trade-offs among compression ratio, reconstruction quality, and computational complexity, with emphasis on their suitability for specific applications. Emerging trends, open research challenges, and potential future directions are highlighted, underscoring the need for scalable, high-performance, and adaptive compression frameworks to meet the growing requirements of next-generation LiDAR applications.