Villadsen algebra is an outstanding class of simple unital AH algebras which have rapid dimension growth. They do not absorb the Jiang-Su algebra, and cannot be classified by the conventional invariant which consists of ordered K-group and the pairing with the trace simplex. However, in the case that the seed space is a given finite dimensional contractable CW complex, the Villadsen algebras, either in the UHF case or in the general AF case, are shown to be classified by the Cuntz semigroup (actually by the order-unit K-group and the comparison radius function). The comparison radius function also can be used to distinguish certain different seed spaces. The talk is based on joint works with George Elliott and Chunguang Li.