Furlan was born to an intellectual and academic family that included a large number of university professors in Zagreb, the capital city of the Republic of Croatia. She was born to a Jewish mother, and a father of Slovenian and Croatian heritage. Furlan graduated from the Academy for Dramatic Arts in Zagreb and holds an equivalent to the BA in theatre. She was a member of the Croatian National Theatre and frequently appeared in Yugoslav television and films, including Cannes Film Festival winner When Father Was Away on Business (1985). In the 1980s, she briefly appeared as singer for Le Cinema, a spin-off from the rock band Film. She has also appeared on the stage in New York and Los Angeles. She has released an album, Songs From Movies That Have Never Been Made. Furlan played Minbari Ambassador Delenn for all five seasons of Babylon 5 and some of the associated TV movies. From 2004-2008 she could be seen playing the character Danielle Rousseau in the ABC television series Lost.