Morphological abnormalities of both the nuclei and the cell bodies of tumour cells were described by Müller in the late 1830s. Abnormalities of mitoses and chromosomes in tumour cells were described in the late 1880s. Von Hansemann, in the 1890s, suggested that tumour cells develop from normal cells because of a tendency to mal-distribution and other changes of chromosomes occurring during mitosis. In the first decades of the 20th century, Mendelian genetics and "gene mapping" of chromosomes were established, and the dominant or recessive bases of the familial predispositions to certain tumour types were recognised. In the same period, the carcinogenic effects of ionising radiations, of certain chemicals and of particular viruses were described. A well-developed "somatic gene-mutational theory" of tumours was postulated by Bauer in 1928. In support of this, in the next three decades, many environmental agents were found to cause mitotic and chromosomal abnormalities in normal cells as well as mutations in germ-line cells of experimental animals. Nevertheless, mitotic, chromosomal, and other mutational theories were not popular explanations of tumour pathogenesis in the first half of the 20th century. Only in the 1960s did somatic mutational mechanisms come to dominate theories of tumour formation, especially as a result of the discoveries of the reactivity of carcinogens with DNA, and that the mutation responsible for xeroderma pigmentosum causes loss of function of a gene involved in the repair of DNA after damage by ultraviolet light (Cleaver in 1968). To explain the complexity of tumourous phenomena, "multi-hit" models gained popularity over "single-hit" models of somatic mutation, and "epigenetic" mechanisms of gene regulation began to be studied in tumour cells. More recently, the documentation of much larger-than-expected numbers of genomic events in tumour cells (by Stoler and co-workers, in 1999) has raised the issue of somatic genetic instability in tumour cells, a field which was pioneered in the 1970s mainly by Loeb. Here these discoveries are traced, beginning with "nuclear instability" though mitotic-and-chromosomal theories, single somatic mutation theories, "multi-hit" somatic theories, "somatic, non-chromosomal, genetic instability" and epigenetic mechanisms in tumour cells as a background to the chapters which follow.