Golf club heads

Putters include a putter body having a ball striking face member made of a material having a first hardness characteristic. A cavity is defined in the putter body behind the ball striking face member, and plural openings are defined in the ball striking face member extending rearward with respect to the ball striking face member and into the cavity. A polymeric material at least partially fills the openings and the cavity, wherein the polymeric material has a second hardness characteristic that is softer than the first hardness characteristic. The ball striking face member and the polymeric material exposed in at least some of the openings provide a ball striking surface of the putter. The ball striking surface may include grooves or scorelines to affect the launch angle, spin, and/or roll of the ball during a putt. Methods for making such putter devices also are described.