Eukaryotic genomes are rich in repetitive DNA sequences grouped in two classes regarding their genomic organization: tandem repeats and dispersed repeats. In tandem repeats, copies of a short DNA sequence are positioned one after another within the genome, while in dispersed repeats, these copies are randomly distributed. In this review we provide evidence that both tandem and dispersed repeats can have a similar organization, which leads us to suggest an update to their classification based on the sequence features, concretely regarding the presence or absence of retrotransposons/transposon specific domains. In addition, we analyze several studies that show that a repetitive element can be remodeled into repetitive non-coding or coding sequences, suggesting (1) an evolutionary relationship among DNA sequences, and (2) that the evolution of the genomes involved frequent repetitive sequence reshuffling, a process that we have designated as a “DNA remodeling mechanism”. The alternative classification of the repetitive DNA sequences here proposed will provide a novel theoretical framework that recognizes the importance of DNA remodeling for the evolution and plasticity of eukaryotic genomes.