I present a short synopsis of (the Gaussian Orthogonal Ensemble, or GOE, of) Random Matrix Theory, and its relevance for Structural Acoustics. It is argued that, if a structure is generic, lacking special symmetries and with dynamics that depends on uncontrolled or unknown details, i.e, is complicated, then its stiffness matrix is—for many purposes—as if it were taken from the Gaussian Orthogonal Ensemble of matrices. Such matrices are symmetric and real with uncorrelated Gaussian entries, and have no preferred directions, that is—it is an ensemble whose statistics are invariant under orthogonal transformations. The consequences are several predictions for the statistics of high frequency responses, including those due to level repulsion, spectral rigidity, and Gaussian random modal amplitudes, predictions that appear to be well satisfied in practice. We discuss why and when the GOE should be relevant to real structures whose stiffness matrices are clearly not, to most appearances, typical members of this ensemble.