Drug resistance is a fundamental problem in the treatment of cancer since cancer that becomes resistant to the available drugs may leave the patient with no therapeutic alternatives. In this chapter, we consider the dynamics of drug resistance in blood cancer and the related issue of the dynamics of cancer stem cells. After describing the main types of chemotherapeutic agents available for cancer treatment, we review the different mechanisms of drug resistance development. Various mathematical models of drug resistance found in the literature are then reviewed. Given the well-known hierarchy of the hematopoietic system, it is critical to focus on those cells that have the ability to self-renew, since these will be the only cells able to induce long-term drug resistance. Thus, a recent mathematical model taking into account the complex dynamics of the leukemic stem-like cells is described. The chapter closes with a few applications of this model to chronic myeloid leukemia.