Abstract: The aim of this talk is to give an overview of the results which can be obtained on the statistical properties of a classical turbulent fluid using Functional Renormalization Group (FRG). I will focus on isotropic, homogeneous and stationary turbulence in incompressible flows, and also passive scalar turbulence. While much effort has been devoted to characterising equal-time properties of the turbulent state, less is known about its temporal behaviour. I will present some analytical results from FRG on the time dependence of generic n-point correlation functions of the turbulent fluid and advected scalars. These results are obtained from first principles, i.e. starting from the Navier-Stokes equation, and advection-diffusion equation for the passive scalar, and are asymptotically exact in the limit of large wave-numbers. I will compare these predictions with available results from both direct numerical simulations and experiments.