The treatment of multiple myeloma is inextricably linked to the need for assessment and monitoring of the minimal residual disease (MRD). Assessment of the MRD allows evaluating the efficacy of therapy and obtaining significant prognostic information; it is an indicator of the degree of eradication of the tumor clone. The methods for detecting residual tumor cells evolve constantly, which translates into updates of the criteria reflecting the scale of response to therapy. There is no single MRD detection technique; common recommendations suggest seeking for pathological cells both intramedullary and extramedullary. This review describes current MDR determination methods, including imaging, next generation multiparametric flow cytometry, and methods based on DNA analysis — allele-specific oligonucleotide polymerase chain reaction and next generation sequencing. We compare their advantages, limitations, disadvantages, clinical significance, and show the necessary sensitivity thresholds of the described methods and the conditions that make this or that approach ideal in the context of detection of MRD.