It is now widely recognized that universal properties of spectral fluctuations for waves in complex or disordered cavities can be accounted for by random matrix theory (RMT). These properties are manifested in short- and long-range correlations of the spectral response. In nondissipative systems, the wave evolution operator may be related to a Hermitian matrix. The lack of information about the system due to complexity or disorder is translated in RMT through statistical ensembles of such matrices (e.g., the Gaussian orthogonal ensemble) in which the only relevant features of the system are its modal density and its global symmetries, such as time-reversal invariance. Here, it is shown that, beyond quantum or electromagnetic systems, these concepts are relevant to acoustics and elastodynamics by presenting the few basics of RMT and a simple argument yielding Wigner’s surmise for the distribution of frequency spacings between neighboring resonances, exemplifying level repulsion. Within the high-frequency geometrical limit of rays, a semiclassical argument due to Berry is sketched for the spectral long-range reduction of fluctuations named spectral rigidity. This is one of the most convincing arguments in favor of the conjecture which stipulates that wave systems which are chaotic in the limit of rays should follow RMT.