Abstract: A surgical milling tool includes a body having a hemispherically-shaped outer surface and defining an internal cavity. Cutting blades carried at spaced locations on the outer surface are operative to mill tissues of a joint socket when the tool is introduced and rotated in the socket. Holes are formed through the outer surface and communicate with the internal cavity to channel cut-off tissues into the cavity as the tool is rotated. A tool support is releasably connected to the tool body to assist in positioning and rotating the body. The support includes a cover which releasably closes the body cavity to retain cut-off tissues within the cavity. Several related tool body and tool support embodiments are described which include structures for releasably drivingly connecting the tool body and the tool support. Some of the embodiments include movable latching elements for securing connections formed between the tool bodies and the tool supports.