Abstract: Multiple zeta values (MZVs) are multi-variable generalizations of the special values of the Riemann zeta function at integers. Their study in the two variable case could be traced back to Euler, but the general study was started by Hoffman and Zagier in early 1990s. A basic question here is to determine the relations among the MZVs. We consider two formulas of Euler, his Factorization Formula and Sum Formula, and discuss their multi-variable generalizations. If time permits, we also illustrate how the renormalization method in quantum field theory can be applied to study divergent MZVs.