Point cloud processing is an essential task in many applications in the AEC domain, such as automated progress assessment, quality control and 3D reconstruction. As much of the procedure used to process the point clouds is shared among these applications, we identify common processing steps and analyse relevant algorithms found in the literature published in the last 5 years. We start by describing current efforts on both progress and quality monitoring and their particular requirements. Then, in the context of those applications, we dive into the specific procedures related to processing point clouds acquired using laser scanners. An emphasis is given to the scan planning process, as it can greatly influence the data collection process and the quality of the data. The data collection phase is discussed, focusing on point cloud data acquired by laser scanning. Its operating mode is explained and the factors that influence its performance are detailed. Data preprocessing methodologies are presented, aiming to introduce techniques used in the literature to, among other aspects, increase the registration performance by identifying and removing redundant data. Geometry extraction techniques are described, concerning both interior and outdoor reconstruction, as well as currently used relationship representation structures. In the end, we identify certain gaps in the literature that may constitute interesting topics for future research. Based on this review, it is evident that a key limitation associated with both Scan-to-BIM and Scan-vs-BIM algorithms is handling missing data due to occlusion, which can be reduced by multi-platform sensor fusion and efficient scan planning. Another limitation is the lack of consideration for laser scanner performance characteristics when planning the scanning operation and the apparent disconnection between the planning and data collection stages. Furthermore, the lack of representative benchmark datasets is hindering proper comparison of Scan-to-BIM and Scan-vs-BIM techniques, as well as the integration of state-of-the-art deep-learning methods that can give a positive contribution in scene interpretation and modelling.