Although the leading dogma for the origin of the diversity in cancer cell subpopulations is based on a stepwise selection and accumulation of genetic changes that allow uncontrollable malignant growth, there is an emerging understanding that the variability of heritable phenotypes in cancer and cancer-prone cells may also involve epigenetic mechanisms. We discuss here experimental data that allow us to postulate that the genome is organized into epigenetic territories with lineage-specific differences in the stringencies of the active and inactive states. Low-stringency epigenetic states are predicted to be closer to mosaicism, or chaos, than high-stringency states. In pathological situations, the result is an epigenetic variability upon which selection mechanisms can act during tumor progression. This view may have significant implications on clinical assessment and prognosis, and also suggests that major factors involved in the resetting and/or maintenance of epigenetic states may serve as new attractive targets for therapeutic interventions.