Theory of collective dynamics: flow, fluctuations and correlations in heavy ion collisions

I review recent developments in the hydrodynamic modeling of ultra-relativistic heavy ion collisions and the extraction of the properties of bulk QCD matter from heavy ion collision measurements. I briefly summarize the current framework used for the theoretical modeling of heavy ion collisions and report the recent progress on the extraction of the temperature dependence of the shear and bulk viscosity coefficients, the development of statistical tools for data-to-model comparison, and anisotropic hydrodynamics. All these recent developments in our field pave the way for more quantitative determination of the transport properties of bulk QCD matter from the experimental heavy ion collision program.