Faithful chromosome segregation during cell division depends on the centromere, a complex DNA/protein structure that links chromosomes to spindle microtubules. This chromosomal domain has to be marked throughout cell division and its chromosomal localization preserved across cell generations. From fission yeast to human, centromeres are established on a series of repetitive DNA sequences and on specialized centromeric chromatin. This chromatin is enriched with the histone H3 variant, named CENP-A, that was demonstrated to be the epigenetic mark that maintains centromere identity and function indefinitely. Although centromere identity is thought to be exclusively epigenetic, the presence of specific DNA sequences in the majority of eukaryotes and of the centromeric protein CENP-B that binds to these sequences, suggests the existence of a genetic component as well. In this review, we will highlight the importance of centromeric sequences for centromere formation and function, and discuss the centromere DNA sequence/CENP-B paradox.