Repetitive DNA is ubiquitous in eukaryotic genomes, but a clear link between its structure, abundance, and biological significance is lacking. There are two main types of repetitive DNA: transposable elements, which are interspersed in the genome, and satellite DNA, which is found in long tandem arrays. Satellite DNA evolves rapidly in sequence and abundance and is rarely conserved between species. In Chapters 2, 3, and 4, I investigate the tandem repeat copy number mutation process using mutation accumulation lines in three diverse species: Daphnia, Chlamydomonas, and mouse. I find that tandem repeats mutate at high rates, but are constrained when selection is at play. In Drosophila virilis, a family of 7 bp satellites have uniquely expanded to take up about half the genome. In Chapter 5, I use comparative genomics and cytogenetics to investigate the satellite expansion in D. virilis and its sister species. I find that the expansion and turnover of sequences was not evenly distributed among satellite family sequences, and selfish processes dominate the dynamics at the centromere. In Chapter 6, I investigate constraints on satellite abundance in D. virilis which I suggest prevent it from expanding beyond around 50% of the genome. I find evidence that satellite abundance influences the rate of DNA breakage and therefore the risk of genome instability events driven by aberrant repair. Finally, an important aspect of studying satellite DNA is overcoming the technical challenges that have existed throughout the history of DNA sequencing. In Chapter 5, I discover satellite-specific biases in several different sequencing platforms and suggest best practices for sequencing satellites. Transposable elements (TEs) are also abundant in genomes, but are more challenging to identify because their sequences are diverse and do not have a fixed structure like genes. In Chapter 7, I present a major update to a TE identification software which accurately recapitulates the TE family composition of any eukaryotic genome. In total, this dissertation presents major contributions to important aspects of satellite DNA evolution using a variety of model species and approaches.