Satellite DNAs represent the most abundant fraction of repetitive sequences in genomes of almost all eukaryotic species. Long arrays of satellite DNA monomers form densely packed heterochromatic genome compartments and also span over the functionally important centromere locus. Many specific features can be ascribed to the evolution of tandemly repeated genomic components. This chapter focuses on the structural and evolutionary dynamics of satellite DNAs and the potential molecular mechanisms responsible for rapid changes of the genomic areas they constitute. Monomer sequences of a satellite DNA evolve concertedly through a process of molecular drive in which mutations are homogenized in a genome and fixed in a population. This process results in divergence of satellite sequences in reproductively isolated groups of organisms. However, some satellite DNA sequences are conserved over long evolutionary periods. Since many satellite DNAs exist in a genome, the evolution of species-specific satellite DNA composition can be directed by copy number changes within a library of satellite sequences common for a group of species. There are 2 important features of these satellite DNAs: long time sequence conservation and, at the same time, proneness to rapid changes through copy number alterations. Sequence conservation may be enhanced by constraints such as those imposed on functional motifs and/or architectural features of a satellite DNA molecule. Such features can limit the selection of sequences able to persist in a genome, and can direct the evolutionary course of satellite DNAs spanning the functional centromeres.