The book chapter will give a short survey about tangential subdifferential and its role in optimization. Firstly, the basic calculus of tangential subdifferential along with relation with other subdifferentials such as Clarke and Michel-Penot subdiferential are considered. Then, the applications of the tangential subdifferential in establishing the optimality conditions and investigating the duality problems of the scalar and multiobjective optimization problems including the state-of-the-art results on the topic are discussed.