A golf ball comprising a core and a cover layer, wherein the cover layer provides one or more deep dimples that extend through the cover layer to and/or into a layer or component underneath is disclosed. The cover may be a single layer or it may include multiple layers. If the cover is a multi-layer cover, the dimples extend to or into at least the first inner cover layer, and may extend to and/or into two or more inner cover layers. If the cover is a single layer, the dimples extend to and/or into the core. The cover layer(s) may be formed from any material suitable for use as a cover, including, but not limited to, ionomers, non-ionomers and blends of ionomers and non-ionomers. The dimples may be spherical or non-spherical, and the portion of the dimple that extends to or into the next inner layer may be the same or different shape as the outer portion of the dimple. Optionally, a moisture barrier layer may be present between the core and/or the cover layer(s).