Numerical solutions of wave scattering problems are important in many scientific and engineering applications. In this talk, we introduce some issues coming from the boundary of wave propagation area during the modeling and simulation. Such issues include the reduction from an unbounded domain to a bounded one, the transmission boundary conditions connecting different wave fields, and wave scattering channel along or between the boundary of nano-structures. We present some results, including the analysis, modeling and numerical results, during dealing with these issues.