Previous experience in the treatment of chronic myeloid leukaemia (CML) has shown that the achievement of clinical, morphological and cytogenetic remission does not indicate eradication of the disease. A complete molecular response (CMR; no detectable BCR-ABL mRNA) represents a deeper level of response, but even CMR is not a guarantee of elimination of the leukaemia, because the significance of CMR is determined by the detection limit of the assay that is used. Two studies of imatinib cessation in CMR are underway, cumulatively involving over 100 patients. The current estimated rate of stable CMR after stopping imatinib is approximately 40%, but the duration of follow-up is relatively short. The factors that determine relapse risk are yet to be identified. The intrinsic capacity of any residual leukaemic cells to proliferate following the withdrawal of treatment may be important, but there may also be a role for immunological suppression of the leukaemic clone. No currently available test can formally prove that the leukaemic clone is eradicated. Here we discuss the sensitive measurement of minimal residual disease, and speculate on the biology of BCR-ABL-positive cells that may persist after effective therapy of CML.