Golf club heads include: (a) a club head body having a ball striking face and defining a rear cavity; (b) a fluid-filled bladder in the cavity; and (c) a retaining member holding the fluid-filled bladder in the cavity. Other club heads include: (a) a club head body having a ball striking face and defining a rear cavity; and (b) an insert member in the rear cavity, wherein the insert member interior includes one or more chambers facing the rear surface of the ball striking face. The chamber(s) may cover at least 30% of a total surface area of the interior surface of the insert member and/or at least 30% of a total interior major surface area of the rear cavity. Golf clubs including these club heads and methods of making such golf clubs and golf club heads also are described.