Available online 8 November 2016 Our aim is to study the modular representation theory of coherent configurations. Let p be a prime. We consider structures of modular adjacency algebras of coherent configurations obtained from combinatorial designs. The structures of standard modules of modular adjacency algebras provide more information than p-ranks of incidence matrices of combinatorial designs. (C) 2016 Elsevier Inc. All rights reserved. Article LINEAR ALGEBRA AND ITS APPLICATIONS. 514:174-197 (2017)