Satellites are one of the most enigmatic parts of the eukaryotic genome. These highly repetitive, noncoding sequences make up as much as half or more of the genomic content and are known to play essential roles in chromosome segregation during meiosis and mitosis, yet they evolve rapidly between closely related species. Research over the last several decades has revealed that satellite divergence can serve as a formidable reproductive barrier between sibling species. Here we highlight several key studies on Drosophila and other model organisms demonstrating deleterious effects of satellites and their rapid evolution on the structure and function of chromosomes in interspecies hybrids. These studies demonstrate that satellites can impact chromosomes at a number of different developmental stages and through distinct cellular mechanisms, including heterochromatin formation. These findings have important implications for how loci that cause postzygotic reproductive isolation are viewed.