Abstract: In 1999, Hampton and Zanette revealed the first synchronization concept for coupled Hamiltonian systems, known as measure synchronization (MS). Since then, there are continued efforts to explore synchronization occurring in Hamiltonian systems, in particular, MS. In this talk, I will briefly overview our research on MS in three different categories of coupled Hamiltonian systems: i) Coupled classical Hamiltonian systems; ii) Coupled quantum Hamiltonian systems; iii) Coupled quantum-classical hybrid systems.