The set of problems that can be solved by new very sensitive method for investigation of surfaces and very thin layers on solids - surface electromagnetic waves (SEW) spectroscopy - is presented. The field of applications for this method was considerably extended with the use of the free electron laser (FEL). The important role of the outstanding facilities of FEL, namely, the broad tuning range, high power, picosecond pulses, narrow bandwidth of emission, well-collimated beam in SEW spectroscopy, is outlined. Interferometric SEW experiments provide the possibility for the direct determination of the real and imaginary parts of dielectric constants at the frequencies inside the tuning range of a FEL, avoiding the Kramers-Kronig integral transformation. It is demonstrated by the examples of infrared absorption spectra of a monomolecular Langmuir-Blodgett film on metal, of a metal oxide film and of polymeric films of nm thicknesses on metals (exposing the effects of chain conformation changes induced by solid surface). In the mid- and far-IR the "reststrahlen" range optical constants of single crystals CaF2, BaF2, MgO, LiNbO3 were determined. The nonlinear spectroscopy applications of SEW-FEL techniques to studies of a second-harmonic generation (SHG) on crystal surfaces in the regime of counterpropagating SEWs - the frequency dependence of efficiency and the influence of a thin film deposition on a quartz surface - are described.