A golf club head for hitting a golf ball toward a target has a directional tendency to launch the golf ball in a selected direction. Basic embodiments include a club head having an asymmetric ball striking face such that one side of the face, as measured from the center of the face, has a first bulge radius and the other side of the face has a second bulge radius. The club head assumes a directional tendency in the direction toward the smaller bulge radius. Other embodiments of club heads with a directional tendency have a striking face with a bulge radius apex shifted either right or left of the center of the striking face such that a club face with the bulge radius apex to the left results in a right directional tendency and a club face with a bulge radius apex to the right results in a left directional tendency. Further embodiments of a club head may include a combination of a shifted bulge radius apex and a different radius on each side of the center of the striking face.