The functional renormalization group provides a new route to study the co-operation and competition between different channels of the interacting systems. Its generalization, multiscale functional renormalization group (MFRG), has recently been shown to be able to capture the results from the Eliashberg theory. In this seminar, I discuss the applications of MFRG on two different electron-phonon interacting systems. 1. The one-dimensional half-filled Holstein-Hubbard model. We show that it does not have any dominant pairing correlation. 2. The effects of electron-phonon coupling in the two-dimensional Hubbard model with a phenomenological band structure for the cuprate superconductors. We show that a momentum-independent electron-phonon coupling does not favor d-wave pairing but instead leads to the s-wave pairing and incommensurate density wave ordering.