In a variety of practical situations such as reverse engineering of boundary representation from depth maps of scanned objects, range data analysis, model-based recognition and algebraic surface design, there is a need to recover the shape of visible surfaces of a dense 3D point set. In particular, it is desirable to identify and fit simple surfaces of known type wherever these are in reasonable agreement with the data. We are interested in the class of quadric surfaces, i.e. algebraic surfaces of degree 2, instances of which are the sphere, the cylinder and the cone. A comprehensive survey of the recent work in each subtask pertaining to the extraction of quadric surfaces from triangulations is presented.