The Runx genes present a challenge to the simple binary classification of cancer genes as oncogenes or tumor suppressors. There is evidence that loss of function of two of the three mammalian Runx genes promotes cancer, but in a highly lineage-restricted manner. In human leukemias, the RUNX1 gene is involved in various chromosomal translocation events that create oncogenic fusion proteins, at least some of which appear to function as dominant-negative inhibitors of the normal gene product. Paradoxically, evidence is mounting that structurally intact Runx genes are also oncogenic when overexpressed. All the three murine genes act as targets for transcriptional activation by retroviral insertional mutagenesis, and the oncogenic potential of Runx2 has been confirmed in transgenic mice. Moreover, the RUNX1 gene is often amplified or overexpressed in cases of acute leukemia. The state of progress in elucidating the oncogenic roles of the Runx genes is the subject of this review, and we draw together recent observations in a tentative model for the effects of Runx deregulation on hematopoietic cell differentiation. We suggest that lineage-specific factors determine the sensitivity to the oncogenic effects of loss or overexpression of Runx factors.