The centriole is a defining feature of many eukaryotic cells. It nucleates a cilium, organizes microtubules as part of the centrosome, and is duplicated in coordination with the cell cycle. Centrioles have a remarkable structure, consisting of microtubules arranged in a barrel with ninefold radial symmetry. At their base, or proximal end, centrioles have unique triplet microtubules, formed from three microtubules linked to each other. This microtubule organization is not found anywhere else in the cell, is conserved in all major branches of the eukaryotic tree, and likely was present in the last eukaryotic common ancestor. At their tip, or distal end, centrioles have doublet microtubules, which template the cilium. Here, we consider the structures of the compound microtubules in centrioles and discuss potential mechanisms for their formation and their function. We propose that triplet microtubules are required for the structural integrity of centrioles, allowing the centriole to serve as the essential nucleator of the cilium.