The idea that tumors must “escape” from immune recognition contains the implicit assumption that tumors can be destroyed by immune responses either spontaneously or as the result of immunotherapeutic intervention. Simply put, there is no need for tumor escape without immunological pressure. Here, we review evidence supporting the immune escape hypothesis and critically explore the mechanisms that may allow such escape to occur. We discuss the idea that the central engine for generating immunoresistant tumor cell variants is the genomic instability and dysregulation that is characteristic of the transformed genome. “Natural selection” of heterogeneous tumor cells results in the survival and proliferation of variants that happen to possess genetic and epigenetic traits that facilitate their growth and immune evasion. Tumor escape variants are likely to emerge after treatment with increasingly effective immunotherapies.