Apparatus and methods for extraction of nails, screws and other such fasteners from wood or other host materials are disclosed. One embodiment of the apparatus includes a shank adapted for application at a rotational drive source, a two-part engaging member at one end of the shank having a cavity extending thereinto for receiving therein a fastener to be extracted and openable to release the fastener after extraction. A cutting component is defined at a bottom edge of the engaging member adjacent to an opening to the cavity for cleanly removing host material from around the fastener. A gripping surface formation comprising a spiraling striation is formed at a surface of the cavity for threadably engaging the fastener to be removed.