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Ten years ago, relativistic viscous fluid dynamics was formulated from firstprinciples in an effective field theory framework, based entirely on theknowledge of symmetries and long-lived degrees of freedom. In the same year,numerical simulations for the matter created in relativistic heavy-ioncollision experiments became first available, providing constraints on theshear viscosity in QCD. The field has come a long way since then. We presentthe current status of the theory of non-equilibrium fluid dynamics in 2017,including the divergence of the fluid dynamic gradient expansion, resurgence,non-equilibrium attractor solutions, the inclusion of thermal fluctuations aswell as their relation to microscopic theories. Furthermore, we review thetheory basis for numerical fluid dynamics simulations of relativistic nuclearcollisions, and comparison of modern simulations to experimental data fornucleus-nucleus, nucleus-proton and proton-proton collisions.

Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions