Kontsevich established a formality theorem and applied it to solve the deformation quantization problem for Poisson manifolds. Following Kontsevich's method, we obtained a formality theorem for dg manifolds. As an application, we extended Duflo theorem in Lie theory to the context of dg manifolds. In this talk, I'll start with an introduction to L-infinity algebras, Kontsevich formality theorem and deformation quantization problem. After that, I plan to explain formality and Kontsevich-Dulfo theorem for dg manifolds.