Cancer cells are highly plastic, favoring adaptation to changing conditions. Genes related to basic cellular processes evolved in ancient species, while more specialized genes appeared later with multicellularity (metazoan genes) or even after mammals evolved. Transcriptomic analyses have shown that ancient genes are up-regulated in cancer, while metazoan-origin genes are inactivated. Despite the importance of these observations, the underlying mechanisms remain unexplored. Here, we study local and global epigenomic mechanisms that may regulate genes from specific evolutionary periods. Using evolutionary gene age data, we characterize the epigenomic landscape, gene expression regulation, and chromatin organization in several cell types: human embryonic stem cells, normal primary B-cells, primary chronic lymphocytic leukemia malignant B-cells, and primary colorectal cancer samples. We identify topological changes in chromatin organization during differentiation observing patterns in Polycomb repression and RNA polymerase II pausing, which are reversed during oncogenesis. Beyond the non-random organization of genes and chromatin features in the 3D epigenome, we suggest that these patterns lead to preferential interactions among ancient, intermediate, and recent genes, mediated by RNA polymerase II, Polycomb, and the lamina, respectively. Our findings shed light on gene regulation according to evolutionary age and suggest this organization changes across differentiation and oncogenesis.