In spite of conspicuous differences in their polarized architecture, swimming unicellular eukaryotes and migrating cells from metazoa display a conserved hierarchical interlocking of the main cellular compartments, in which the microtubule network has a dominant role. A microtubule array can organize the distribution of endomembranes owing to a cell-wide and polarized extension around a unique nucleus-associated structure. The nucleus-associated structure in animal cells contains a highly conserved organelle, the centriole or basal body. This organelle has a defined polarity that can be transmitted to the cell. Its conservative mode of duplication seems to be a core mechanism for the transmission of polarities through cell division.