The classical human satellite DNAs, also referred to as human satellites 1, 2 and 3 (HSat1, HSat2, HSat3, or collectively HSat1–3), occur on most human chromosomes as large, pericentromeric tandem repeat arrays, which together constitute roughly 3% of the human genome (100 megabases, on average). Even though HSat1–3 were among the first human DNA sequences to be isolated and characterized at the dawn of molecular biology, they have remained almost entirely missing from the human genome reference assembly for 20 years, hindering studies of their sequence, regulation, and potential structural roles in the nucleus. Recently, the Telomere-to-Telomere Consortium produced the first truly complete assembly of a human genome, paving the way for new studies of HSat1–3 with modern genomic tools. This review provides an account of the history and current understanding of HSat1–3, with a view towards future studies of their evolution and roles in health and disease.