A point cloud is a set of 3D points defined by X, Y & Z coordinates. Point clouds are most often created by 3D laser scanners. These devices measure a large number of points on the surface of an object or a scene, and output a point cloud as a data file. The point cloud represents the visible surface of the object that has been scanned or digitized. In our research, we are interested in recovering the underlying geometrical structure from 3D point clouds. Specifically, we focus on three major geometries that are commonly seen in most man-made structure, such as planes, cylinders, and cones. The research is formulated as a statistical inference problem where we adopt both traditional Expectation Maximization (EM) algorithms as well as more powerful Markov Chain Monte Carlo methods. Given the 3D structure, another important topic is texture mapping that adds detailed surface texture and color. We want to investigate how to perform structure-guided texture mapping that will align the 3D geometrical primitives with the observed 2D features (such lines or corners). The major applications of this research include high-definition surveying and 3D structure modeling, such bridges or industrial facilities.