Chronic myeloid leukemia (CML) is the paradigm for targeted cancer therapy. RT-qPCR is the gold standard for monitoring response to tyrosine kinase-inhibitor (TKI) therapy based on the reduction of blood or bone marrow BCR-ABL1. Some patients with CML and very low or undetectable levels of BCR-ABL1 transcripts can stop TKI-therapy without CML recurrence. However, about 60 percent of patients discontinuing TKI-therapy have rapid leukaemia recurrence. This has increased the need for more sensitive and specific techniques to measure residual CML cells. The clinical challenge is to determine when it is safe to stop TKI-therapy. In this review we describe and critically evaluate the current state of CML clinical management, different technologies used to monitor measurable residual disease (MRD) focus on comparingRT-qPCR and new methods entering clinical practice. We discuss advantages and disadvantages of new methods.