They played in Cleveland, Ohio, at Gund Arena between 2001 and 2006.

The Barons name was revived in 2001 when the San Jose Sharks purchased their AHL affiliate, the Kentucky Thoroughblades, and relocated them to Cleveland, where they would play at the arena which was owned and operated by Sharks owners George and Gordon Gund.

The Gunds had also owned the NHL Barons, who played in the NHL in the late 1970s before being merged with the Minnesota North Stars in 1978.

Dan Gilbert, owner of the Cleveland Cavaliers of the National Basketball Association (NBA), purchased the inactive Utah Grizzlies AHL franchise and moved it to Cleveland.

The team logo, a shark holding a hockey stick, was originally designed as an alternate logo for the San Jose Sharks before being modified with a top hat, a monocle, and formal wear for the Barons.