Some embodiments include club heads having reinforced club head faces. In one example, the club head comprises a variable face thickness with thickened and thinned regions. The face includes a thinned perimeter region positioned near a perimeter of the face, and a thickened central region positioned over a geometric center of the face. The club head further comprises a 360 undercut that extends along the entire perimeter of the face. The combination of the thinned perimeter region, thickened central region, and 360 undercut reinforces the club head while permitting the face to bend. Other embodiments of related club heads and methods are also disclosed.