Recent improvement in the methods of chromosome analysis has allowed recognition of consistent chromosome alterations in several human cancers, especially leukemias and lymphomas. At the same time, newly discovered human cellular oncogenes have been mapped to individual chromosomes, with precise band assignment. Some of the assignments are coincident with the breakpoints of translocations observed in particular tumors. In fact, a relocation of the corresponding oncogenes has been observed in the cells of some of these tumors. Two notable examples are that of the t(9;22) translocation of chronic myelogenous leukemia (CML), causing the transfer of the oncogene c-abl from chromosome 9 to chromosome 22, and that of the t(8;14) translocation of Burkitt lymphoma, causing the transfer of the oncogene c-myc from chromosome 8 to chromosome 14. These findings can be taken as indicative of a critical role of chromosome alterations in the origin of cancer, through the activation of one or more cellular oncogenes, although there is no firm evidence that such an activation actually occurs. In addition, some concern exists over the validity of accepting in vitro transformation of a cell line by oncogenes as a model of carcinogenesis in man. For these reasons the question on the significance of chromosome alterations in leukemias and lymphomas should not be considered entirely settled yet. Useful models, whose study may lead to the clarification of this important point, are represented by premalignant conditions, such as the myeloproliferative disorders, where chromosome abnormalities are present before the development of a bona fide neoplasm, and by the aneuploidy syndromes, in which there exists an association between a constitutional chromosome anomaly and an increased risk of cancer.