Satellite DNA represents one of the most fascinating parts of the repetitive fraction of the eukaryotic genome. Since the discovery of highly repetitive tandem DNA in the 1960s, a lot of literature has extensively covered various topics related to the structure, organization, function, and evolution of such sequences. Today, with the advent of genomic tools, the study of satellite DNA has regained a great interest. Thus, Next-Generation Sequencing (NGS), together with high-throughput in silico analysis of the information contained in NGS reads, has revolutionized the analysis of the repetitive fraction of the eukaryotic genomes. The whole of the historical and current approaches to the topic gives us a broad view of the function and evolution of satellite DNA and its role in chromosomal evolution. Currently, we have extensive information on the molecular, chromosomal, biological, and population factors that affect the evolutionary fate of satellite DNA, knowledge that gives rise to a series of hypotheses that get on well with each other about the origin, spreading, and evolution of satellite DNA. In this paper, I review these hypotheses from a methodological, conceptual, and historical perspective and frame them in the context of chromosomal organization and evolution.