The covering type is a combinatorial invariant recently introduced by Karoubi & Weibel in 2016. It has been studied on topological spaces X denoted ct(X), it is the minimal number of open contractible subsets covering Y where Y ranges over the set of topological spaces homotopically equivalent to X. In this talk, I will talk about KW-complexity for finite presentation groups which, by abuse of language, is the covering type of groups. Then I will give you some examples of applications.