We describe the constraint satisfaction problem and show that it unifies a very wide variety of computational problems. We discuss the techniques that have been used to analyse the complexity of different forms of constraint satisfaction problem, focusing on the algebraic approach, explaining the basic ideas and highlighting some of the recent results in this area. The above abstract belongs to a joint invited talk at FTP & Tableaux 2009. The full version of the paper is included in [1]. 1. P. Jeavons. Presenting constraints. In M. Giese and A. Waaler, editors, Automated Reasoning with Analytic Tableaux and Related Methods, 18th International Conference, TABLEAUX 2009, volume 5607 of Lecture Notes in Computer Science, pages 1-15. Springer, 2009.