  Shear viscosity is a dynamical property of fluid systems close to
equilibrium, describing resistance to sheared flow. After reviewing the physics
of viscosity and the reason it is usually difficult to compute, I discuss its
importance within the theory of QCD and the obstacles to carrying out such a
computation. A diagrammatic analysis requires extensive resummations and even
then convergence is poor at physically relevant couplings. Lattice approaches
require a poorly controlled analytical continuation of data from the Euclidean
to the Minkowski domain. At present our best results for QCD shear viscosity
come from the hydrodynamical interpretations of experiments, with
first-principles calculations trailing behind.
