The failures of engineered dams that retain freshwater or mining waste (tailings) have led to socioeconomic and environmental consequences. However, the global magnitude-frequency statistics of these occurrences remain poorly quantified, out-of-date and/or limited in scope. Addressing this gap would give insight into how the hazard-risk of water-retention (reservoir) dams and mine tailings impoundments has evolved over time, and would provide quantitative benchmarks for estimating likelihoods of facility failures and their societal impacts to support risk assessments. In this study, we analyze new datasets and estimates of the construction and failures of large reservoir facilities (LRFs) and tailings storage facilities (TSFs) worldwide in the period 1965–2020. We address long-standing data gaps on LRF failures in China, and subsequently worldwide, and on constructed TSFs worldwide by adopting multiple estimation/extrapolation approaches to illustrate the range of uncertainty in our results. The total number of LRF failures is estimated to have been between 394 and 608. The annual numbers of newly constructed and failed LRFs declined near-proportionally, thus the cumulative failure rate of LRFs stayed fairly constant, falling in the range of 1.2% to 1.8% as of end-of-2020. The rate drops to at least 0.7% when excluding China. The cumulative fatality rate of LRFs reduced over time to 1.2 deaths per constructed facility, and falls in the range of 64 to 98 deaths per failure, as of end-of-2020. Failures of LRFs with very high storage capacities (>200 million m³) have continued to occur since 2016. The annual number of TSF failures stayed relatively constant, whereas the annual construction rate of TSFs is estimated to have increased by ~3×, thus the cumulative failure rate of TSFs declined over time. When assuming our lower-estimate of the number of constructed TSFs (6810), the cumulative failure rate is ~4.4% as of end-of-2020. When adopting our upper-estimate (20,230 TSFs), we obtain a rate of ~1.5%, which falls in the same order as the corresponding rate of LRFs. Our review of published estimates of existing TSFs worldwide indicates that the “true” rate is much lower than 4.4% and closer to 1.5%. The cumulative fatality rates of TSF failures reduced over time to 0.1–0.3 death per constructed facility and 6 deaths per failure as of end-of-2020, which are lower than those of LRFs. However, the size and the environmental impact of TSF failures have increased on average worldwide, especially since 2014. The rising global rate of failed tailings volumes has been approximately proportional to the rising global rate of tailings production since the 1990s. Heavy rainfall events and intensifying precipitation patterns are statistically important causative variables for the failures of both LRFs and TSFs. This has implications for the design and management of storage capacity, freeboard, facility drainage and spillways under climate change conditions. Our results are applicable broadly on a global scale and are conditioned by uncertainties in the data and the methods used to address data gaps. To improve the robustness of future statistical analyses, a more comprehensive public disclosure effort is necessary, particularly with respect to reservoir facility failures in China and constructed TSFs worldwide.