Let X be a compact metric space and T:-> X be continuous.  Let h^*(T) be the supremum of sequence entropies of T over all subsequences of N and S(X) be the set of h^*(T) for all continuous maps T on X.  We want to find out the relation between S(X) and the topology structure of the space X.  In this talk I will introduce some of the recent results about this subject.