In past papers, Gauss indicated his desire to study the spherical images of parabolic points of surfaces, that is points where the Gaussian curvature is zero. Gauss never published any results in this regard, and so this paper examines parabolic points and cusps of Gauss mappings. In particular, we give ten geometric characterizaions of cusps of Gauss mappings, a discussion of elliptic and hyperbolic cusps, and applications of singularity theory to differential geometry.