Operad is a structure consists of operations and their compositions. Each operad defines a type of algebra, e.g. associative algebras, commutative algebras and Lie algebras. The Koszul dual of operads then serves as a bridge between different types of algebras. This formalism has been proven to be powerful in many domains like topology and algebraic geometry. In this Quid seminar, I would like to tell some stories about Koszul duality and its use in knot theory and Galois theory.