Coarsening systems, such as the phase separation dynamics that follows
a rapid quench into an unstable region of the phase diagram, exhibit
critical-like behavior. At late times, the system evolves into a
self-similar state with a length scale that grows as a power of time L~t^alpha.
This growth exponent is highly universal, depending only on conservation laws
and the nature of the order parameter. A dynamical renormalization group fixed point
provides the natural scenario for understanding these features, but unfortunately
no systematic RG approach exists for this problem. Further, recent exact solutions
have made clear that the universality classes for the growth exponent and the
correlation function differ. We are then faced with the problem of determining
universality classes for a strong coupling RG fixed point. I will present a
survey of the available results, a strategy for how to proceed, and a conjecture
for coarsening universality classes.