Surface wave propagation can be exploited to investigate subsurface conditions in terms of shear wave velocities in a number of possible applications (geotechnical site characterisation, seismic-risk assessment, crustal studies and non-destructive testing). Nowadays, one of the most common methods adopted to analyse the dispersion of surface waves is based on the determination of the Rayleigh wave frequency-dependent phase velocities obtained from multichannel active data. The obtained values represent the dispersion curve, which is inverted to determine the vertical shear-wave velocity (V_S) profile. After briefly recalling some fundamental facts and problems regarding surface wave propagation and analysis, we present the Full Velocity Spectrum (FVS) approach which here is used to jointly invert the velocity spectra of the Rayleigh and Love waves acquired by means of a set of horizontal geophones only (Rayleigh waves are in fact analysed while considering their radial component). It is shown that for non-trivial data sets for which modal dispersion curves cannot be soundly extracted, the joint FVS approach may represent an efficient way to properly analyse the data, thus eventually obtaining a robust V_S profile free from significant ambiguities that would otherwise inevitably affect the results obtained by following the ordinary approach based on the modal dispersion curve(s) of just one component.