An essential factor of low-dimensional systems is the relatively strong role of the electron-lattice interaction, which e.g. is involved in CDW phase transitions. The electron energies can be drastically changed by the electron-phonon interaction, resulting in the formation of heavy electrons dressed by phonons, known as quasiparticles. This effect tends to be rather pronounced in surface states. With the aid of high-resolution ARPES this effect can be explored quantitatively. In our group we use such data to evaluate energy scale and coupling strength. The electron-phonon interaction can provide insight about the energy of adsorbate vibrations, e.g. on adsorbed metal surfaces. In electron gases on semiconductor surfaces, this can be a hint on the relative role of the lattice in electronically driven phase transitions.