Trivium is a bit oriented synchronous stream cipher designed by Cannière and Preneel. It is one of the eSTREAM hardware-oriented finalists and an International Standard under ISO/IEC 29192-3:2012. Cube attacks are an important type of key recovery attack against Trivium. First, I will give a survey on cube attacks against Trivium. Second, I will present our recent results including an algebraic method for recovering superpolies and observations that some best key recovery attacks given by division property based cube attacks are distinguishing attacks.