Collectively, various tandem and interspersed repetitive sequences make up approximately half the human genome, yet we have only begun to understand the potential functions of “junk” DNA. Here, we provide a brief overview of various types of repeats, but a full treatment of the repeat genome (repeatome) is beyond the scope of any review. Hence, we focus primarily on less established functions of a few major repeat classes, including pericentromeric satellites and abundant degenerate interspersed repeats, short interspersed nuclear elements (Alu), and long interspersed nuclear elements (L1). A theme developed throughout is how sequence organization in the human karyotype provides insights into potential functions within nuclear structure. For example, millions of small tandem major satellite repeats can form bodies that sequester nuclear factors, or the segmental organization of interspersed repeats may underpin the nuclear compartmentalization of heterochromatin and euchromatin. Decoding the vast repeatome is an exciting frontier being enabled by recent technological advancements. However, identifying the extent of meaningful information in repeats will likely require concepts that go well beyond impacts for individual genes, to new ways to identify and interpret broad patterns of genome-wide organization and nucleus-wide regulation.