Proper chromosome segregation during cell division is essential for proliferation, and this is facilitated by kinetochores, large protein complexes assembled on the centromeric region of the chromosomes. Although the sequences of centromeric DNA differ totally among organisms, many components of the kinetochores assembled on centromeres are very well conserved among eukaryotes. To define the identity of centromeres, centromere protein A (CENP-A), which is homologous to canonical histone H3, acts as a landmark for kinetochore assembly. Kinetochores mediate spindle–microtubule attachment and control the movement of chromosomes during mitosis and meiosis. To conduct faithful chromosome segregation, kinetochore assembly and microtubule attachment are elaborately regulated. Here we review the current understanding of the composition, assembly, functions and regulation of kinetochores revealed mainly through studies on fission and budding yeasts. Moreover, because recent cumulative evidence suggests the importance of the regulation of the orientation of kinetochore–microtubule attachment, which differs distinctly between mitosis and meiosis, we focus especially on the molecular mechanisms underlying this regulation.