(1) Background: New therapeutic strategies have improved the prognosis of multiple myeloma (MM), changing the accepted view of this disease from being incurable to treatable. (2) Methods: We studied 1001 patients with MM between 1980 and 2020, grouping patients into ten-year periods by diagnosis 1980–1990, 1991–2000, 2001–2010 and 2011–2020. (3) Results: After 65.1 months of follow-up, the median OS of the cohort was 60.3 months, and OS increased significantly over time: 22.4 months in 1980–1990, 37.4 months in 1991–2000, 61.8 months in 2001–2010 and 103.6 months in 2011–2020 (p < 0.001). Using novel agents in the front-line setting for myeloma patients yielded a significantly better OS than in those treated with conventional therapies, especially when combinations of at least two novel agents were used. The median OS of patients treated with the combination of at least two novel agents in induction was significantly prolonged compared to those treated with a single novel agent or conventional therapy in induction: 143.3 vs. 61.0 vs. 42.2 months (p < 0.001). The improvement was apparent in all patients regardless of age at diagnosis. In addition, 132 (13.2%) patients were long-term survivors (median OS ≥ 10 years). Some independent clinical predictors of long-term survival were identified: ECOG < 1, age at diagnosis ≤ 65 years, non-IgA subtype, ISS-1 and standard-risk cytogenetic. Achieving CR and undergoing ASCT were positively associated with >10 years of survival. (4) Conclusions: The combination of novel agents appears to be the main factor for the improvement in survival in MM, which is becoming a chronic and even curable disease in a subtype of patients without high-risk features.