Stochastic dynamics play a central role in strongly coupled phenomena. We present and review a theory independent approach in holography to study such phenomena. We firstly argue that the heavy quark diffusion occurs in realistic strongly coupled systems. Then we analyze the quantum and thermal fluctuation, dissipation and the corresponding Brownian motion of a heavy particle in such environments for a wide class of theories. The holographic study is based on the properties of the straight string fluctuations. The observables and coefficients associated with the stochastic motion depend on a single parameter which encodes the properties of the different theories. Moreover, certain Dp-brane fluctuations can be mapped one-to-one to the string fluctuations and therefore the stochastic brane observables can be read from the string ones.

Then we review the Langevin diffusion of a moving heavy quark in generic thermal holographic theories. The analysis is based on the properties of the trailing string and its fluctuations. The string world-sheet has a black hole horizon and the quarks feels an effective temperature different than the environmental one. The formulas of the effective temperature, the drag force on the particle and the Langevin coefficients are given in terms of the background metric elements readily applicable to any theory. At the end we comment on the backreaction effects on the medium and present results of the Monte Carlo simulations.