Chronic myeloid leukemia has been drastically changed by the introduction of targeted therapies in the 2000s. Currently, one of the challenging question is how to decide wether one can stop therapy or not. We will see how our models can give insights on the underlying mechanisms responsible for success or failure of treatment cessation. We will especially discuss the hypothesis of an important role of the immune system in this result. We will also review how some different models suggest the patients might be overtreated.