Point-to-line mappings (PTLMs) have several uses in image analysis and computer vision; a linear PTLM was used by Hough to detect sets of collinear points in an image, and it can be shown that three lines L, M, N in the plane are the images of three mutually perpendicular lines in space iff there exists a PTLM that maps the vertices of triangle LMN into their opposite sides. This paper discusses a variety of mathematical properties of PTLMs. It begins by reviewing some facts about linear PTLMs, with emphasis on their point-line incidence properties, and discusses canonical forms for the matrices of such PTLMs. It then shows that any PTLM that has an incidence-symmetry property must be linear and must have a symmetric matrix. It also discusses PTLMs of polygons, and shows how to construct polygons whose vertices are mapped into their sides by a PTLM. Finally, it shows how a PTLM can be used to define binary operations on points, and discuss algebraic properties of these operations.