For every class of polycrystalline materials, the scientific study of grain boundaries as well as the increasingly widespread practice of grain boundary engineering relies heavily on visual representation for the analysis of boundary statistics and their connectivity. Traditional methods of grain boundary representation neglect the full complexity of misorientation information and often rely on boundary classification schemes of dubious physical significance. This talk will highlight my recent work toward significantly advancing our ability to represent grain boundary information. Beginning with an understanding of the topology of the group space of misorientations, we developed new methods of mapping and visualizing boundary character. This new technique allows micrographs or maps of grain boundaries to be presented in a colorized form which, at a glance, reveal all of the misorientation information in an entire grain boundary network, as well as the connectivity among different boundary misorientations. Finally, I will introduce the extension of recently developed hyperspherical harmonic formulation for the description of grain boundary misorientation and boundary-plane statistics. These new and improved methods of representing grain boundary information, which are already being incorporated in commercial software packages, are expected to be powerful tools for grain boundary network analysis as the practice of grain boundary engineering becomes a routine component of the materials design paradigm.