Perovskite-structure AMnO3 manganites played an important role in the development of numerous physical concepts such as double exchange, small polarons, electron-phonon coupling, and Jahn-Teller effects, and they host a variety of important properties such as colossal magnetoresistance and spin-induced ferroelectric polarization (multiferroicity). A-site-ordered quadruple perovskite manganites AMn7O12 were discovered shortly after, but at that time their exploration was quite limited. Significant progress in their understanding has been reached in recent years after the wider use of high-pressure synthesis techniques needed to prepare such materials. Here we review this progress, and show that the AMn7O12 compounds host rich physics beyond the canonical AMnO3 materials.