The geometry of lines in 3-space has been a part of the body of classical algebraic geometry since the pioneering work of Plücker. Interest in this branch of geometry has been revived by several converging trends in computer science. The discipline of computer graphics (Chapter 52) has pursued the task of rendering realistic images by simulating the flow of light within a scene according to the laws of elementary optical physics. In these models light moves along straight lines in 3-space and a computational challenge is to find efficiently the intersections of a very large number of rays with the objects comprising the scene. In robotics (Chapters 50 and 51) the chief problem is that of moving 3D objects without collisions. Effects due to the edges of objects have been studied as a special case of the more general problem of representing and manipulating lines in 3-space. Computational geometry (whose core is better termed “design and analysis of geometric algorithms”) has moved in the nineties from the realm of planar problems to tackling directly problems that are specifically 3D. The new and sometimes unexpected computational phenomena generated by lines (and segments) in 3-space have emerged as a main focus of research.