Novel and more effective treatment strategies against multiple myeloma (MM) have significantly prolonged patients' survival and raised interest in the depth of response and its association with clinical outcome. Minimal residual disease (MRD) has emerged as one of the most relevant prognostic factors in MM and should be included in a new definition of complete response (CR). Although further standardization is still required, MRD monitoring should be applied in prospective clinical trials as a sensitive tool to compare and evaluate the efficacy of different treatment strategies, particularly in the consolidation and maintenance settings, and implement individualized therapy-monitoring approaches. Here, we review current definition of deep response in MM, advantages and limitations of current MRD assessment assays, clinical evidences for MRD monitoring as a prognostic tool for therapeutic decisions in MM, and challenges to develop uniform criteria for MRD monitoring.