Wood-type golf club heads include: (a) a club head body including heel, toe, crown, sole, and weighted rear portions; and (b) a variable thickness ball striking face. The club head body parts and weighted portion(s) may be arranged such that the club head has a moment of inertia about a vertical axis passing through the club head center of gravity of at least 5000 g-cm2. Such club heads may include: (a) a cup face member including a ball striking face portion and a return portion; (b) sole and crown portions engaged with the return portion; (c) a rear body member engaged with the crown and/or sole portions; (d) a weight member at the club head rear; and/or (e) a hosel member engaged with the cup face member, the crown portion, and/or the sole portion. Methods of making such club heads also are described.