  We review aspects of classical and quantum mechanics of many anyons confined
in an oscillator potential. The quantum mechanics of many anyons is complicated
due to the occurrence of multivalued wavefunctions. Nevertheless there exists,
for arbitrary number of anyons, a subset of exact solutions which may be
interpreted as the breathing modes or equivalently collective modes of the full
system. Choosing the three-anyon system as an example, we also discuss the
anatomy of the so called ``missing'' states which are in fact known numerically
and are set apart from the known exact states by their nonlinear dependence on
the statistical parameter in the spectrum.
  Though classically the equations of motion remains unchanged in the presence
of the statistical interaction, the system is non-integrable because the
configuration space is now multiply connected. In fact we show that even though
the number of constants of motion is the same as the number of degrees of
freedom the system is in general not integrable via action-angle variables.
This is probably the first known example of a many body pseudo-integrable
system. We discuss the classification of the orbits and the symmetry reduction
due to the interaction. We also sketch the application of periodic orbit theory
(POT) to many anyon systems and show the presence of eigenvalues that are
potentially non-linear as a function of the statistical parameter. Finally we
perform the semiclassical analysis of the ground state by minimizing the
Hamiltonian with fixed angular momentum and further minimization over the
quantized values of the angular momentum.
