Golf clubs and golf club heads, such as putter heads, may include a putter body and an insert forming a ball striking face and engaged with the putter body. Portions of the insert may be formed of a metal material, while portions of the insert may be formed of a polymer material. The insert may include a base portion having grooves or openings formed therein. This base may be joined with another material (such as a polymer backing material) to form the insert, wherein the backing material at least partially fills the grooves or openings. In some arrangements, the backing material of the insert may be visible at the top and/or bottom surfaces of the putter structures. Methods for making such putter devices are also described.