Tumor escape from the host immune response remains the major problem holding the development of immunotherapies for cancer. In this review, congenic mouse lines are discussed that differ dramatically in their ability to respond to tumors tested and, thereby, to survive or to succumb to the tumor and/or its metastases. This ability is under the control of either MHC class I or nontrivial MHC class II beta genes expressed in a small subpopulation of antigen-presenting cells. Two hypotheses can explain the results obtained so far: (1) emergence of tumor cell variants that escape the host immune response in morbid mice but are eliminated in survivors, and (2) tumor-induced immunosuppression, which is either efficient or not, depending on the congenic line used. It is argued that further experimentation on these congenics will allow to choose the correct hypothesis, and to characterize the mechanism(s) of elimination of minimal residual disease and prevention of tumor escape by the immune system of survivors as well as the reason(s) for its failure in morbid mice. It is also argued that the use of these models will substantially increase the chance to resolve the controversy of poor correlation of immunotherapy testing in mice with clinical results.