  Around 1950, Wigner introduced the idea of modelling physical reality with an
ensemble of random matrices while studying the energy levels of heavy atomic
nuclei. Since then, the field of random-matrix theory has grown tremendously,
with applications ranging from fluctuations on the economic markets to complex
atomic spectra. The purpose of this short article is to review several attempts
to apply the basic concepts of random-matrix theory to the structure and
radiative transitions of atoms and ions, using the random matrices originally
introduced by Wigner in the framework of the gaussian orthogonal ensemble. Some
intrinsic properties of complex-atom physics, which could be enlightened by
random-matrix theory, are presented.
