  The subject area referred to as "wave chaos", "quantum chaos" or "quantum
chaology" has been investigated mostly by the theoretical physics community in
the last 30 years. The questions it raises have more recently also attracted
the attention of mathematicians and mathematical physicists, due to connections
with number theory, graph theory, Riemannian, hyperbolic or complex geometry,
classical dynamical systems, probability etc. After giving a rough account on
"what is quantum chaos?", I intend to list some pending questions, some of them
having been raised a long time ago, some others more recent.
