Furlan was a member of the Croatian National Theatre and frequently appeared in Yugoslavian television and films, including Cannes Film Festival winner When Father Was Away on Business (1985). Her best-known American role is as Minbari Ambassador Delenn in the television series Babylon 5. She has also appeared on the Los Angeles stage, and released an album "Songs From Movies That Have Never Been Made". Furlan is married to director Goran Gajic, who has directed her in an episode of Babylon 5 and several plays, including a production of Sophocles' Antigone.