The closed geodesics are the most common objects between Geometry and Dynamics area, which play an important role during the development of mathematics. In this talk, I will try to tease out all the previous researches of closed geodesic problems in different point of views. Many famous theories will be touched, such as the min-max method, Morse theory, Index theory and so on.  But, since I will focus the closed geodesic problems themselves, there will be no much details included.