Satellite DNAs (tandemly repeated, non-coding DNA sequences) stretch over almost all native centromeres and surrounding pericentromeric heterochromatin. Once considered as inert by-products of genome dynamics in heterochromatic regions, recent studies showed that satellite DNA evolution is interplay of stochastic events and selective pressure. This points to a functional significance of satellite sequences, which in (peri)centromeres may play some fundamental functional roles. First, specific interactions with DNA-binding proteins are proposed to complement sequence-independent epigenetic processes. The second role is achieved through RNAi mechanism, in which transcripts of satellite sequences initialize heterochromatin formation. In addition, satellite DNAs in (peri)centromeric regions affect chromosomal dynamics and genome plasticity. Paradoxically, while centromeric function is conserved through eukaryotes, the profile of satellite DNAs in this region is almost always species-specific. We argue that tandem repeats may be advantageous forms of DNA sequences in (peri)centromeres due to concerted evolution, which maintains high intra-array and intrapopulation sequence homogeneity of satellite arrays, while allowing rapid changes in nucleotide sequence and/or composition of satellite repeats. This feature may be crucial for long-term stability of DNA-protein interactions in centromeric regions.