Centrioles are cylinders made of nine microtubule (MT) triplets present in many eukaryotes. Early studies, where centrosomes were seen at the poles of the mitotic spindle led to their coining as "the organ for cell division". However, a variety of subsequent observational and functional studies showed that centrosomes might not always be essential for mitosis. Here we review the arguments in this debate. We describe the centriole structure and its distribution in the eukaryotic tree of life and clarify its role in the organization of the centrosome and cilia, with an historical perspective. An important aspect of the debate addressed in this review is how centrioles are inherited and the role of the spindle in this process. In particular, germline inheritance of centrosomes, such as their de novo formation in parthenogenetic species, poses many interesting questions. We finish by discussing the most likely functions of centrioles and laying out new research avenues.