Golf club and golf club head structures include an inner wall or backstop arranged behind a ball striking surface of the golf club head and defining a gap between the inner wall and a rear surface of the ball striking surface. In some arrangements, the size of the gap may vary along a heel-to-toe length of the inner wall or backstop. For instance, the size of the gap may gradually increase from a first end of the inner wall toward a central region of the inner wall, and may gradually decrease from the central region toward a second end of the inner wall. In some examples, the inner wall or backstop may be connected to the golf club head, for instance, at a first end and/or a second end.