Centromeres are essential regions of eukaryotic chromosomes responsible for the formation of kinetochore complexes, which connect to spindle microtubules during cell division. Notably, although centromeres maintain a conserved function in chromosome segregation, the underlying DNA sequences are diverse both within and between species and are predominantly repetitive in nature. The repeat content of centromeres includes high-copy tandem repeats (satellites), and/or specific families of transposons. The functional region of the centromere is defined by loading of a specific histone 3 variant (CENH3), which nucleates the kinetochore and shows dynamic regulation. In many plants, the centromeres are composed of satellite repeat arrays that are densely DNA methylated and invaded by centrophilic retrotransposons. In some cases, the retrotransposons become the sites of CENH3 loading. We review the structure of plant centromeres, including monocentric, holocentric, and metapolycentric architectures, which vary in the number and distribution of kinetochore attachment sites along chromosomes. We discuss how variation in CENH3 loading can drive genome elimination during early cell divisions of plant embryogenesis. We review how epigenetic state may influence centromere identity and discuss evolutionary models that seek to explain the paradoxically rapid change of centromere sequences observed across species, including the potential roles of recombination. We outline putative modes of selection that could act within the centromeres, as well as the role of repeats in driving cycles of centromere evolution. Although our primary focus is on plant genomes, we draw comparisons with animal and fungal centromeres to derive a eukaryote-wide perspective of centromere structure and function.