Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) allows us to acquire vibrational signals at surfaces. In STM-IETS, a tunneling electron from the STM tip excites vibrations whenever the energy of tunneling electron exceeds the vibrational energies. This opens up an inelastic channel in parallel with the elastic one and gives rise to an increase/decrease of the conductivity in the STM junction. As a consequence, a pair of peak and dip shows up at the bias voltages with respect to the Fermi level corresponding to the energy of vibrational energy. Until recently, the application of STM-IETS was limited to the localized vibration of single atoms and molecules adsorbed on surfaces. In principle, STM-IETS should be capable of detecting the collective lattice dynamics, i.e., phonons. In this talk, I will introduce the example STM-IETS measurement for surface and interface phonons and provides the theoretical analysis behind them. The surface phonon on Cu(110) and interface phonons relevant of graphene on SiC substrate are good examples. In the former part, I will provide theoretical formalism about the electron-phonon coupling upon the electron tunneling based on a simple model Hamiltonian. In the latter case, we discuss the spatial dependence of the IETS spectrum induced by the excitation of the interface phonons based on the ab initio calculations..