This paper deals with the local exact boundary controllability for dynamics governed by nonlinear wave equations, subject to Dirichlet, Neumann, or any other kind of boundary controls which result in well- posedness of the corresponding initial- boundary value problem. A constructive method is developed. The local exact boundary controllability for semilinear wave equations is constructed in the case of both three ( odd) and two ( even) space dimensions, and the boundary control is time optimal when the space dimension is three ( odd). Especially, the local exact boundary controllability is established for quasi- linear wave equations in several space dimensions by using the constructive method.