Generic and non-generic features of billiards and nuclei which show up in certain spectral properties are discussed by way of selected examples. Firstly, the short- and long-range correlations of levels belonging to the magnetic dipole Scissors Mode in heavy deformed nuclei at an excitation energy of about 3 MeV prove that this mode is indeed caused by an ordered or regular collective motion. Secondly, the fine structure distribution of the so-called electric Pygmy Dipole Resonance around 6-7 MeV excitation energy seems to indicate a situation where the spectral properties are governed by mixed dynamics, i.e. by regular and chaotic features. However, in nuclei quantitative conclusions are always severely hampered by missing levels due to limited experimental resolution and detector efficiency. Thirdly, it is shown that this situation can be largely overcome by studying spectral properties in superconducting microwave billiards considered as nuclear analogues. As an example resonance strength distributions in billiards of mixed and fully chaotic dynamics are considered. Finally, it is demonstrated how symmetry breaking effects in nuclei--e.g. isospin symmetry breaking--can be studied through those resonance strength distributions by modelling the nuclear problem with coupled billiards.