  We discuss the impact of recent developments in the theory of chaotic
dynamical systems, particularly the results of Sinai and Ruelle, on microwave
experiments designed to study quantum chaos. The properties of closed Sinai
billiard microwave cavities are discussed in terms of universal predictions
from random matrix theory, as well as periodic orbit contributions which
manifest as `scars' in eigenfunctions. The semiclassical and classical Ruelle
zeta-functions lead to quantum and classical resonances, both of which are
observed in microwave experiments on n-disk hyperbolic billiards.
