Putter heads have a ball striking face portion and a rear body portion (as one or more parts). These putter heads may have a DCG/B ratio of at least 0.425 (where B is the overall breadth dimension and DCG is the depth of the center of gravity). Some putter heads may include: (a) a ball striking face body member having a ball striking face with plural openings defined in its central portion; (b) a polymeric material mostly located behind an exterior surface of the ball striking face, wherein a portion of the polymeric material is exposed at the exterior surface of the ball striking face through the openings; and (c) a rear body member engaged with the ball striking face body member. Rear body members or portions thereof can be interchanged to allow for customization and/or better fitting of the putter to the user's putting stroke and/or tastes.