Since the nonlocal measurement is helpful in discovering nontrivial physics that is too difficult to detect directly, the nonlocal measurement has now become one of the research focuses in condensed matter physics. Recent experiments find the signal of the giant nonlocal resistance in an H-shaped multi-terminal graphene system. After excluding other possible transport mechanisms, such as the classic Ohmic diffusion and the edge states, researchers tend to believe that the nonlocal resistance signal originates from the spin/valley Hall effect existing in graphene sample. Based on the Landauer-Buttiker formula, the numerical results make a relatively perfect match with the experimental data in the same multi-terminal graphene system. However, though the theoretic research has made certain progress in explaining the existence of the nonlocal resistance, it is still difficult to understand some exotic behaviors of the nonlocal resistance, which exhibits properties even contradictory to the known classical theories. For instance, the nonlocal resistance decreases to zero much more rapidly than the local one, and the giant peak of the nonlocal resistance appears inside the energy gap of the graphene. In this review, the experiments focusing on the nonlocal resistance in multi-terminal graphene system are carefully reviewed. Besides, this review also shows the associated theoretic studies, and an overlook of the future study is also provided.