In this talk, I first give a basic introduction to AdS/CFT and then explore the formalism of AdS/CFT in the long wavelength regime to show the relation between bulk configurations obeying Einstein's equations and holographic fluid configurations obeying the Navier-Stokes equation. As a concrete example, we will explore black branes in $\operatorname{AdS}_5$ and examine their long wavelength dynamics in thecontext of the fluid-gravity correspondence.