Dominantly heritable susceptibility is known for virtually every cancer. Susceptibility is typically restricted to one or a few tumours. For some tumours there appear to be at least two different predisposing conditions. Some mutant gene carriers survive to old age without developing the expected tumour(s). Some cases are new germline mutations. None of the conditions is very common, because of natural selection against gene carriers. Two questions arise: What is inherited? What is the relationship between the hereditary and non-hereditary forms of the same tumour? Retinoblastoma is a prototypic tumour. Penetrance in humans is nearly complete by the age of five years in the heritable form, which usually affects both eyes. Rare cases in which there is a constitutional deletion of chromosomal band 13q14 permitted localization of the responsible gene. Tumour formation is clearly a rare event at the cellular level, suggesting the necessity of a second, somatic, event. The difference in ages at diagnosis between unilateral and bilateral cases also suggests that two somatic events occur in non-hereditary cases. One explanation is that the gene is recessive and the second event involves loss of the remaining normal allele by mutation, non-disjunction, deletion or somatic recombination. The normal allele may be regarded as anti-oncogenic.