Material flow analysis (MFA), a central methodology of industrial ecology, quantifies the ways in which the materials that enable modern society are used, reused, and lost. Sankey diagrams, termed the "visible language of industrial ecology", are often employed to present MFA results. This Perspective assesses the history and current status of MFA, reviews the development of the methodology, presents current examples of metal, polymer, and fiber MFAs, and demonstrates that MFAs have been responsible for creating related industrial ecology specialties and stimulating connections between industrial ecology and a variety of engineering and social science fields. MFA approaches are now being linked with environmental input-output assessment, scenario development, and life cycle assessment, and these increasingly comprehensive assessments promise to be central tools for sustainable development and circular economy studies in the future. Current shortcomings and promising innovations are also presented, as are the implications of MFA results for corporate and national policy.