This book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021. The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation systems; analysis of diagrams; diagrams and computation; cognitive analysis; diagrams as structural tools; formal diagrams; and understanding thought processes. 10 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book constitutes the refereed proceedings of the 13th International Conference on the Theory and Application of Diagrams, Diagrams 2022, held in Rome, Italy, in September 2022. The 11 full papers and 19 short papers presented together with 5 posters were carefully reviewed and selected from 58 submissions. 8 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.