Autonomous vehicles rely on their perception systems to understand their surroundings. However, the evolution of autonomous navigation technologies has led to new security issues. LiDAR sensors are crucial for autonomous vehicles, and this paper presents the first study that focuses exclusively on attacks and defense mechanisms on this device. This survey comparatively analyzes the attacks and mitigation techniques in state-of-the-art according to their complexity and robustness. The main LiDAR datasets in the literature are described, and trending approaches for future research directions based on the included solutions are discussed. Overall, this work provides a comprehensive overview of LiDAR attacks and their potential threats. It is an essential contribution to LiDAR security and will help to inform the development of countermeasures.