We develop efficient computational methods for the interface problem in the planar symmetric radiative transfer equation with isotropic scattering. Numerical schemes are developed for both the transport-transport coupling and the transport-diffusion coupling through the interfaces at which waves can reflect and (diffusively) transmit. We also study high frequency wave problems. A level set method is developed to capture the Keller-Maslov phase shift for the computation of multivalued solutions in the high frequency limit. We also numerically study the semiclassical limit of the Schrodinger-Poission equations and use it to select the unique weak solution to the Vlasov-Poisson equations.