This book constitutes the refereed proceedings of the Third International Workshop on Asynchronous Many-Task Systems and Applications, WAMTA 2025, held in St. Louis, Missouri, USA during February 19–21, 2025. The 13 full papers and 2 short papers included in this book were carefully reviewed and selected from 18 submissions. The WAMTA 2025 conference proceedings help developers, users, and proponents of these models and systems share experience, discuss how they meet the challenges posed by Exascale system architectures, and explore opportunities for increased performance, robustness, productivity, and full-system utilization.