Mitochondria and plastids in eukaryotic cells contain distinct genomes and multiply in the cytoplasm by binary division of preexisting organelles. Mitochondrial and plastid nuclei are easily visualized as compartments in the matrix of organelles by high-resolution fluorescence microscopy and by immunoelectron microscopy using anti-DNA antibodies. Plastid and mitochondrial division can be clearly separated into two main events: division of the organelle nuclei, and then division of the rest of the organelles, the process of organellokinesis (mitochondriokinesis and plastidokinesis). The mechanical apparatus that regulates organellokinesis has remained undetermined. In 1986, the plastid-dividing apparatus (PD ring) for plastidokinesis was first identified by us in the primitive red alga Cyanidium caldarium RK-1. The PD ring is located in the cytoplasm outside the organelle envelope at the constricted isthmus of dividing organelles and has subsequently been found in all eukaryotic plants examined. We were also the first to identify the mitochondrion-dividing apparatus (MD ring) for mitochondriokinesis in the unicellular red alga Cyanidioschyzon merolae in 1993. Eukaryotic cell division is therefore controlled by at least three dividing apparata (rings), a contractile ring, an MD ring, and a PD ring, while bacterial division is controlled by a single bacterial contractile FtsZ ring. The aims of this review are to present the fine structure, process of formation, and contraction of the organelle-dividing apparatus, focusing on evolutionary conservation and diversion from the bacterial contractile ring.