  Luminous galaxies and their dark halos are likely to have triaxial shapes.
The construction of distribution functions for triaxial systems is a hard
problem, due to the existence of only one exact integral of motion, the energy
$E$. Even so, progress has been made by use of analytic methods for special
potentials, numerical combination of orbit densities (Schwarzschild's method),
and N-body simulations. Despite these efforts, we are a long way from
understanding -- let alone constructing -- the full variety of models needed to
interpret the photometric and kinematic data on galaxies that is now available.
Some of the main unsolved problems include the range of intrinsic shapes and
figure rotation speeds for which stable dynamical equilibria can be built, and
the dynamical role of cusps and central black holes.
