The three volume set LNCS 13155, 13156, and 13157 constitutes the refereed proceedings of the 21st International Conference on Algorithms and Architectures for Parallel Processing, ICA3PP 2021, which was held online during December 3-5, 2021. The total of 145 full papers included in these proceedings were carefully reviewed and selected from 403 submissions. They cover the many dimensions of parallel algorithms and architectures including fundamental theoretical approaches, practical experimental projects, and commercial components and systems. The papers were organized in topical sections as follows:Part I, LNCS 13155: Deep learning models and applications; software systems and efficient algorithms; edge computing and edge intelligence; service dependability and security algorithms; data science; Part II, LNCS 13156: Software systems and efficient algorithms; parallel and distributed algorithms and applications; data science; edge computing and edge intelligence; blockchain systems; deept learning models and applications; Io T; Part III, LNCS 13157: Blockchain systems; data science; distributed and network-based computing; edge computing and edge intelligence; service dependability and security algorithms; software systems and efficient algorithms.