What do we know about the shear-viscosity of QCD matter?

The success of ideal Relativistic Fluid Dynamics (RFD) in describing hadron spectra and elliptic flow at RHIC has led to a strong interest in the transport coefficients of QCD, in particular the shear- and bulk-viscosity as well as the shear-viscosity over entropy-density ratio η/s. Of course ideal RFD assumes η to be zero, which is unphysical, but its success has hinted at a very small value for η/s. The purpose of this post is to review what we currently know about η/s of QCD matter and put the different approaches used to study this quantity into context.