We consider the scattering problem for the nonlinear Schrödinger equation with linear potentials. In particular, we mainly focus on the case where both of nonlinearities and potentials are of long-range type in the sense of scattering. In this talk, we introduce a concrete form of the asymptotic behavior of solutions of this equation and show the modified scattering for the associated final state problem, as well as the existence of modified wave operators. This talk is based on the joint work with Haruya Mizutani (Osaka University).