I'll talk about tannakian theory for enhanced triangulated categories, i.e., stable infinity-categories. Tannakian theory for stable infinity-categories is formulated by means of derived algebraic geometry. I'll start with several motivating backgrounds, e.g., classicalGalois/Tannaka theory, motivic Galois theory of mixed motives, homotopy theory, and an informal introduction to derived algebraic geometry. If time permits, applications will be described.