This book constitutes the refereed proceedings of the Second International Joint Conference on Conceptual Knowledge Structures, CONCEPTS 2025, held in Cluj-Napoca, Romania, during September 8-12, 2025. The 25 full papers and 2 short papers included in this book were carefully reviewed and selected from 33 submissions. They were organized in topical sections as follows: Methodology; Patterns, Clusters, Visualization and Software; Data Analysis; and Theory. .