The centromere is the genetic locus required for chromosome segregation. It is the site of spindle attachment to the chromosomes and is crucial for the transfer of genetic information between cell and organismal generations. Although the centromere was first recognized more than 120 years ago, little is known about what determines its site(s) of activity, and how it contributes to kinetochore formation and spindle attachment. Recent work in this field has supported the hypothesis that most eukaryotic centromeres are determined epigenetically rather than by primary DNA sequence. Here, we review recent studies that have elucidated the organization and functions of centromeric chromatin, and evaluate present-day models for how centromere identity and propagation are determined.