Drinking water is essential to public health and socioeconomic growth. Therefore, assessing and ensuring drinking water supply is a critical task in modern society. Conventional approaches to analyzing and controlling drinking water quality are labor-intensive and costly with a low throughput. Machine learning (ML) is an alternative, promising technique to assess and ensuring safe drinking water supply. Existing reviews have summarized the applications of ML in safe drinking water supply from different aspects. However, a state-of-the-art, comprehensive review is missing that focuses on applying ML to monitor, simulate, predict, and control drinking water quality, especially in municipal engineered water systems. This review, therefore, critically compiles the applications of ML in assessing and ensuring water quality in engineered water systems. To be comprehensive, we also cover the applications of ML in other drinking-water-related settings such as water sources and water purification processes. We explain the basic mechanics and workflows of ML, focusing on the applications of ML to access and control key factors or etiologies in drinking water from the physical, chemical, and microbiological aspects. Those factors or etiologies affect water quality and public health, such as water pipeline failures, disinfectant by-products, heavy metals, opportunistic pathogens, biofilms, and antimicrobial resistance genes. We then illustrate the distribution of ML models across research topics in safe drinking water supply. Finally, we discuss the challenges and outlooks for the applications of machine learning in safe drinking water supply. This is the first review summarizing the feasibility and applications of ML in assessing and ensuring water quality in municipal engineered water systems as well as other related water environments.