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LiDAR is a commonly used sensor for autonomous driving to make accurate, robust, and fast decision-making when driving. The sensor is used in the perception system, especially object detection, to understand the driving environment. Although 2D object detection has succeeded during the deep-learning era, the lack of depth information limits understanding of the driving environment and object location. Three-dimensional sensors, such as LiDAR, give 3D information about the surrounding environment, which is essential for a 3D perception system. Despite the attention of the computer vision community to 3D object detection due to multiple applications in robotics and autonomous driving, there are challenges, such as scale change, sparsity, uneven distribution of LiDAR data, and occlusions. Different representations of LiDAR data and methods to minimize the effect of the sparsity of LiDAR data have been proposed. This survey presents the LiDAR-based 3D object detection and feature-extraction techniques for LiDAR data. The 3D coordinate systems differ in camera and LiDAR-based datasets and methods. Therefore, the commonly used 3D coordinate systems are summarized. Then, state-of-the-art LiDAR-based 3D object-detection methods are reviewed with a selected comparison among methods.