In chronic myeloid leukemia (CML), the presence of a specific chromosome marker (Ph-chromosome) as well as of the corresponding molecular marker (BCR-ABL fusion transcripts) provides suitable and precise tools to monitor the burden of the disease present at diagnosis and that of the residual disease present at specific time points during treatment. A huge number of studies have clearly demonstrated that in CML cytogenetic and molecular responses are strictly correlated to the final outcome of the patients and the correct use of standardized methods to assess the achievement of specific degrees of disease reduction at specific time points during treatment has become an essential part of proper clinical management of CML. The target to be achieved and the corresponding "optimal response" definition are however evolving, and at least for some patients, they may be represented not only by best possible overall survival (OS) but also by the possibility to discontinue the tyrosine-kinase inhibitor (TKI) treatment and therefore to live in a treatment-free remission (TFR) status. Therefore, at least for some patients, deep degrees of molecular response, as MR(4) and MR(4.5), whose precise definition has been recently introduced and that are prerequisites to try to discontinuation, are becoming the target to be achieved even in common clinical practice. As a fast initial decline of the disease burden after therapy start may be highly predictive for the final outcome of patients not only in terms of progression-free survival (PFS) and of PS but also in terms of possibility of achieving deep molecular responses, a more intense and punctual monitoring of the response of CML patients during the first 6 months of TKI therapy is now recommended by the more recent versions of the European Leukemia Net (ELN) and National Comprehensive Cancer Network (NCCN) guidelines, as this represents the major driver to decide therapy.