The classical Koszul theory plays an important role in the representation theory of graded algebras. However, there are a lot of structures (algebras, categories, etc) having natural gradings with non-semisimple degree 0 parts, to which the classical theory cannot apply. Particular examples include polynomial rings over non-semisimple algebras, extension algebras of modules, etc. In this talk I'll introduce a generalized Koszul theory which does not demand the semisimple property. It preserves many classical results as Koszul duality and has a close relation to the classical one. Applications of this generalized theory to extension algebras of modules and modular skew group algebras will be described.