Higher-order spectral (HOS) analysis tools are employed to extract the nonlinear dynamic response features of elastic and laminated plates by using both physics-based mechanical plate models and experimental data. Bispectral and trispectral densities are computed to highlight the presence and relative importance of quadratic and cubic nonlinearities. The former are associated with the presence of asymmetry either in the excitation or in the mechanical response of predeflected plates while the latter are due to midplane stretching effects. Besides the detection of these structural nonlinearities in perfect (baseline) fully clamped plates, the changes of such nonlinearities induced by the presence of small inertial imperfections (i.e., lumped masses) are identified and exploited to localize the imperfections. The numerical and experimental investigations are carried out both on isotropic and laminated composite plates subject to Gaussian white noise excitation. The effectiveness of the HOS-based procedure for detection of the nonlinearities is fully demonstrated for both types of plates.