Abstract: The history of the equivalence principle（EP） is reviewed, and the weak EP (Galileo′s EP), strong EP (Einstein′s EP), and very strong EP are explained. Experiments show that EP has not been violated up to an experimental accuracy of 10-13. In the last part of the paper we point out the insufficiency of general relativity, which cannot describe the coupling between the spin of matter and the gravitational field. As we know, a spin particle or a rotating body can be characterized by an asymmetric energy-momentum tensor and a spin tensor. However, the gravitational field equations in general relativity only involve the symmetric components but not the asymmetric part of the former tensor, nor are there any contributions from the latter tensor. On the other hand, a gauge theory (with torsion) of gravitation does include the coupling of spin with the gravitation field. The theory predicts that the motion for a spin particle or a rotating body would deviate from a geodesic one, and hence violate EP. In order to test this violation we suggest experiments in both a laboratory on the Earth and a satellite in space.