In this talk, we focus on simple smooth modules over , where  is the Lie superalgebra of polynomial vector fields on . We first study the Kac module over a finite-dimensional Lie superalgebra , which is an induced module from a simple module over a certain finite-dimensional Lie algebra. We determine the simplicity of such module, and its submodules and quotient modules when it is not simple. Then based on these results, we classify all simple smooth -modules. We also give a characterization of simple smooth-modules. In addition, we describe all Whittaker vectors and submodules of the universal Whittaker -module. These results are from joint works with Professor Rencai Lü.