Early cell biologists perceived centrosomes to be permanent cellular structures. Centrosomes were observed to reproduce once each cycle and to orchestrate assembly a transient mitotic apparatus that segregated chromosomes and a centrosome to each daughter at the completion of cell division. Centrosomes are composed of a pair of centrioles buried in a complex pericentriolar matrix. The bulk of microtubules in cells lie with one end buried in the pericentriolar matrix and the other extending outward into the cytoplasm. Centrioles recruit and organize pericentriolar material. As a result, centrioles dominate microtubule organization and spindle assembly in cells born with centrosomes. Centrioles duplicate in concert with chromosomes during the cell cycle. At the onset of mitosis, sibling centrosomes separate and establish a bipolar spindle that partitions a set of chromosomes and a centrosome to each daughter cell at the completion of mitosis and cell division. Centriole inheritance has historically been ascribed to a template mechanism in which the parental centriole contributed to, if not directed, assembly of a single new centriole once each cell cycle. It is now clear that neither centrioles nor centrosomes are essential to cell proliferation. This review examines the recent literature on inheritance of centrioles in animal cells.