This article is a survey on representation theory of association schemes including recent developments and some applications. A lot of known formulas on complex characters are also obtained as corollaries to results Oil finite dimensional semisimple algebras. Clifford theory of association schemes and related results are explained. Also this article contains basic parts of modular representation theory. Modular representation theory is new and remarkable method in this area. Some open questions and related results are given. (C) 2008 Elsevier Ltd. All rights reserved.