There is considerable interest in developing techniques to detect and/or quantify remaining leukaemia cells termed measurable or, less precisely, minimal residual disease (MRD) in persons with acute myeloid leukaemia (AML) in complete remission defined by cytomorphological criteria. An important reason for AML MRD-testing is the possibility of estimating the likelihood (and timing) of leukaemia relapse. A perfect MRD-test would precisely quantify leukaemia cells biologically able and likely to cause leukaemia relapse within a defined interval. AML is genetically diverse and there is currently no uniform approach to detecting such cells. Several technologies focused on immune phenotype or cytogenetic and/or molecular abnormalities have been developed, each with advantages and disadvantages. Many studies report a positive MRD-test at diverse time points during AML therapy identifies persons with a higher risk of leukaemia relapse compared with those with a negative MRD-test even after adjusting for other prognostic and predictive variables. No MRD-test in AML has perfect sensitivity and specificity for relapse prediction at the cohort- or subject levels and there are substantial rates of false-positive and -negative tests. Despite these limitations, correlations between MRD-test results and relapse risk have generated interest in MRD-test result-directed therapy interventions. However, convincing proof that a specific intervention will reduce relapse risk in persons with a positive MRD-test is lacking and needs testing in randomized trials. Routine clinical use of MRD-testing requires further refinements and standardization/harmonization of assay platforms and results reporting. Such data are needed to determine whether results of MRD-testing can be used as a surrogate end point in AML therapy trials. This could make drug-testing more efficient and accelerate regulatory approvals. Although MRD-testing in AML has advanced substantially, much remains to be done.