By a Torelli class, we mean a symplectic mapping class acting trivially on homology. The study of symplectic Torelli groups has been a central topic of modern symplectic topology. In this talk, we embark on a voyage of Torelli classes and entropies. It turns out that Floer theory can genuinely detect a positive topological entropy, namely that there is a Torelli class in a symplectic K3 surface having a positive topological entropy. This is joint work with Myeonggi Kwon.