The successful 80s musical set in Vietnam is "Miss Saigon". It tells the story of a young Vietnamese woman named Kim, who falls in love with an American soldier named Chris during the Vietnam War. The musical explores themes of love, loss, and the impact of war on individuals and families. "Miss Saigon" features memorable songs such as "The Heat is On in Saigon," "I'd Give My Life For You," and "Last Night of the World." The show opened on Broadway in 1991 and ran for over a decade. It has since been produced in numerous countries around the world, becoming one of the most popular and successful musicals of all time.