Abstract Repetitive DNA sequences, as transposable elements (TEs) and satellite DNA (satDNA) spread and diversify within host genomes, impacting genome biology in numerous ways. In the first part of this review, we emphasize the evolutionary importance of satDNAs and TEs, providing a short summary of their roles and the mechanisms by which they influence the structure and function of genomes. We also discuss the broad, complex, and extensive relationships between TEs and satDNAs. Following that, we bring together different mechanisms on the generation of satDNA from TE, as it has been demonstrated that almost any part of any type of TE can undergo tandemization and produce novel satDNAs. Importantly, we here present a hypothesis that would explain the existence of particular types of monomers, namely composite satDNA monomers which display multiple subsequent stretches of similarity to various TEs, for which the explanation was lacking so far. We propose that even highly shuffled and degraded TE remnants residing in heterochromatin ‘TE graveyards’ can give rise to new satDNA sequence monomers, transforming these genomic loci into DNA ‘recycling yards’. Furthermore, we emphasize important evolutionary questions regarding the causes, mechanisms, and frequency of these occurrences.