Brownian motion is a paradigmatic stochastic process, and well studied both theoretically as well as experimentally. A natural occurance of Brownian motion is found for micron sized particles immersed in simple, Newtonian fluids. The motion of this particle is then a (nearly) perfect random walk, and obeys a linear (Markovian) stochastic equation. This is not true if the particle is suspended in a viscoelastic fluid, which is characterized by long relaxation times and pronounced nonlinear properties. The latter case if thus a good model system for nonlinear stochastic processes, and studying it is challenging, both theoretically as well experimentally. For example, driving the particle drives the viscoelastic fluid out of equilibrium, so that Brownian motion in a non-equilibrium bath is obtained. We will discuss recent theoretical and experimental progress regarding this scenario.