The centromere is the DNA region that ensures genetic stability and is therefore of vital importance. Paradoxically, centromere proteins and centromeric structural domains are conserved despite that fact that centromere DNA sequences are highly variable and are not conserved. Remarkably, heritable states at the centromere can be propagated independent of the underlying centromeric DNA sequences. This review describes the epigenetic mechanisms governing centromere behavior, i.e., the mechanisms that control centromere assembly and propagation. A centromeric histone variant, CenH3, and histone modifications play key roles at centromeric chromatin. Histone modifications and RNA interference are important in assembly of pericentric heterochromatin structures. The molecular machinery that is directly involved in epigenetic control of centromeres is shared with regulation of gene expression. Nucleosome remodeling factors, histone chaperones, histone-modifying enzymes, transcription factors, and even RNA polymerase II itself control epigenetic states at centromeres.