The epidemiology, genetics/genomics and molecular biology of cancer all point to the involvement of a large number of genes in the malignant progression of the vast majority of human cancers. Our current conceptual models of cancer are discussed here and are integrated with an assessment of the strategies required for treating and potentially curing human cancers driven by multiple genome abnormalities. There are settings in which excellent responses will be seen in cancers driven primarily by single genomic abnormalities, e.g., imatinib in chronic myeloid leukemia and gastrointestinal stromal tumors. Other multigenic cancers will require drug cocktails or single drugs acting on multiple downstream targets.