  Experiments with superconducting microwave cavities have been performed in
our laboratory for more than two decades. The purpose of the present article is
to recapitulate some of the highlights achieved. We briefly review (i) results
obtained with flat, cylindrical microwave resonators, so-called microwave
billiards, concerning the universal fluctuation properties of the eigenvalues
of classically chaotic systems with no, a threefold and a broken symmetry; (ii)
summarize our findings concerning the wave-dynamical chaos in three-dimensional
microwave cavities; (iii) present a new approach for the understanding of the
phenomenon of dynamical tunneling which was developed on the basis of
experiments that were performed recently with unprecedented precision, and
finally, (iv) give an insight into an ongoing project, where we investigate
universal properties of (artificial) graphene with superconducting microwave
photonic crystals that are enclosed in a microwave resonator, i.e., so-called
Dirac billiards.
