Kinetic theory and transport coefficients of hot QCD

One of the main findings of the experimental program on ultrarelativistic heavy ion collisions
is that the produced medium appears to have a very small shear viscosity to entropy ratio. 
After an introduction to the subject I will review the challenges in the theory description, focussing in particular on the effective
kinetic theory approach, which allows to compute both the transport coefficients, such as the shear viscosity,
and the medium modifications to jets, another striking finding of the experimental program.  
After introducing the main features of the kinetic framework, which requires
the assumption of weak coupling, I will review the recent results in extending such approach to next-to-leading
order, so that one can estimate the uncertainties that arise when extrapolating to realistic couplings. 
I will also compare the weak-coupling results with the holographic results and I will discuss the relevance of the methods I present for early-universe cosmology.