In this talk, we are concerned with the second order quasilinear strictly hyperbolic equations with quadratic nonlinearity and small non-compactly supported initial data. Especially, for the general Klein-Gordon equations without any null conditions, we establish the global existence of smooth solutions for the 3D case and the almost global existence for the 2D case in the standard Sobolev spaces. These works are joint with Dr. Hou Fei and Dr. Tao Fei.