Vectorization is an important process in the fields of graphics and image processing. In computer-aided design (CAD), drawings are scanned, vectorized and written as CAD files in a process called paper-to-CAD conversion or drawing conversion. In geographic information systems (GIS), satellite or aerial images are vectorized to create maps. In graphic design and photography, raster graphics can be vectorized for easier usage and resizing. Vector arts are popular as online contents. Vectorization takes raster images, point clouds, or a series of scattered data samples in space, outputs graphic elements of various types including points, lines, curves, polygons, parametric curves and surface patches. The vectorized representations consist of a different set of components and elements from that of the inputs. The change of representation is the key difference between vectorization and practices such as smoothing and filtering. Compared to the inputs, the vector outputs provide higher order of control and attributes such as smoothness. Their curvatures or gradients at the points are scale invariant and they are more robust data sources for downstream applications and analysis. This dissertation explores and broadens the scope of vectorization in various contexts. I propose a novel vectorization algorithm on raster images along with several new applications for vectorization mechanism in processing and analysing both 2D and 3D data sets. The main components of the research are: using vectorization in generating 3D models from 2D floor plans; a novel raster image vectorization methods and its applications in computer vision, image processing, and animation; and vectorization in visualizing and information extraction in 3D laser scan data. I also apply vectorization analysis towards human body scans and rock surface scans to show insights otherwise difficult to obtain.