Amber was born in Los Angeles, California. Her parents are from Taiwan. She has one older sister named Jackie. She attended El Camino Real High School in California prior to moving to Korea to be a trainee under S.M. Entertainment.
Liu was cast from S.M. Entertainment's Los Angeles global audition in 2008, where she and one male were selected to be trainees for SM Entertainment. After a year and a half of training, she debuted under the new South Korean girl group f(x) in September 2009, labeled as "Asia's Pop Dance Group." On September 1, 2009, f(x)'s first single "LA chA TA" was digitally released. They debuted on September 2 at their very own showcase event held at the Samseong-dong Fashion Center. The group's first broadcast performance of "LA chA TA" was held at MBC's music show Show! Music Core on September 5, 2009. Months after, they released their first single album Chu~♡, consisting of three songs. On May 4, 2010, they finally released their first mini albumNu ABO. The song, Goodbye Summer, from f(x)'s second album, Pink Tape, was composed by Liu together with the songwriter, Gen Neo of NoizeBank. Her latest published work is the song Summer Lover which is included in f(x)'s newly released third album, Red Light, in collaboration with Sean Alexander.
During Go f(x), Amber revealed that her parents initially had mixed feelings regarding her music career. She stated: "My dad was very cautious, at first ...but then my mom was always supportive from the beginning. I really thank her and she also convinced my dad".
Liu has been confirmed to be part of the new cast of the second season of Invincible Youth, a Korean variety show, in which her fellow f(x) member, Victoria, was a part of during the show's first season. Liu and Woori (from Rainbow) have been confirmed to be leaving Invincible Youth 2. Liu and Woori will be focusing on their group activities - Liu will be focusing on the Japan debut and Korean comeback and Woori will be focusing activities in Japan with her group.