Mobile Laser Scanning (MLS) is a versatile remote sensing technology based on Light Detection and Ranging (lidar) technology that has been utilized for a wide range of applications. Several previous reviews focused on applications or characteristics of these systems exist in the literature, however, reviews of the many innovative data processing strategies described in the literature have not been conducted in sufficient depth. To this end, we review and summarize the state of the art for MLS data processing approaches, including feature extraction, segmentation, object recognition, and classification. In this review, we first discuss the impact of the scene type to the development of an MLS data processing method. Then, where appropriate, we describe relevant generalized algorithms for feature extraction and segmentation that are applicable to and implemented in many processing approaches. The methods for object recognition and point cloud classification are further reviewed including both the general concepts as well as technical details. In addition, available benchmark datasets for object recognition and classification are summarized. Further, the current limitations and challenges that a significant portion of point cloud processing techniques face are discussed. This review concludes with our future outlook of the trends and opportunities of MLS data processing algorithms and applications.