Wood-type golf club heads include: (a) a ball striking face member; and (b) a club head body attached to or integrally formed with the face member. One body component of the club head (e.g., a weight or cover member) may be formed from a transparent, partially transparent, or translucent material. In some club head structures, an external weight member may extend around a part of a club head body member and beyond or outside of at least a portion of the body member's exterior perimeter (e.g., rearwardly, laterally toward a toe side, and/or laterally toward a heel side of the club head body, beyond the exterior perimeter portion, when viewed from overhead). Golf club structures that include golf club heads, e.g., of the types described above, and methods of constructing and/or using such clubs and club heads, also are described.