Multiple myeloma (MM) is still considered an incurable hematologic cancer and, in the last decades, the treatment goal has been to obtain a long-lasting disease control. However, the recent availability of new effective drugs has led to unprecedented high-quality responses and prolonged progression-free survival and overall survival. The improvement of response rates has prompted the development of new, very sensitive methods to measure residual disease, even when monoclonal components become undetectable in patients’ serum and urine. Several scientific efforts have been made to develop reliable and validated techniques to measure minimal residual disease (MRD), both within and outside the bone marrow. With the newest multidrug combinations, a good proportion of MM patients can achieve MRD negativity. Long-lasting MRD negativity may prove to be a marker of “operational cure”, although the follow-up of the currently ongoing studies is still too short to draw conclusions. In this article, we focus on results obtained with new-generation multidrug combinations in the treatment of high-risk smoldering MM and newly diagnosed MM, including the potential role of MRD and MRD-driven treatment strategies in clinical trials, in order to optimize and individualize treatment.