Abstract: Multiple Dirichlet Series arise in certain applications to estimate special values of L-functions. In general, these series are functions of several complex values and exhibit a multiplicativity which allows us to specify coefficients for powers of a single prime. However, this multiplicativity is "twisted" by certain arithmetic symbols and introduces some interesting characteristics. We will look briefly at some examples of Multiple Dirichlet series including the Weyl Group Multiple Dirichlet series.