The prognosis and clinical outcomes for patients with multiple myeloma have improved significantly over the past two decades. A substantial number of patients now achieve complete remission after induction therapy, and more sensitive methods are needed to assess response. Minimal or measurable residual disease (MRD) has been incorporated in many clinical trials as well as in clinical practice. The importance of MRD assessment and correlation between MRD negativity and prolonged progression-free and overall survival has been confirmed in numerous clinical trials and several meta-analyses. Recent studies have even suggested that MRD negativity can partly overcome the impact of the negative prognostic factors such as high-risk cytogenetics or adverse revised international scoring system (R-ISS) stage. MRD can be measured in the bone marrow via imaging and via emerging blood-based techniques. The most common methods are multicolor flow cytometry and next-generation sequencing of bone marrow samples. Using these methods in optimal settings, MRD negativity with a sensitivity level of 10−6 can be detected. In this review, we discuss the benefits and limitations of these techniques as well as the clinical implications.