Abstract: Active complex fluid systems like living cells, assemblies of motors and filaments, flocks of birds, and vibrated granular material are nonequilibrium systems that consume and dissipate energy.

These active systems exhibit phenomena that can be quite distinct from those of conventional equilibrium soft materials. Nevertheless, their long-wavelength properties can at times be described by hydrodynamic-like stochastic equations similar to those of equilibrium systems but with additional terms that break Onsager reciprocity and noise sources that violate the fluctuation dissipation theorem. In this talk, we focus on a model active system, namely, a bacterial bath, which consists of a population of rod-like motile or self-propelled bacteria suspended in a fluid environment. We discuss results of recent microrheological experiments in terms of a dynamical model for nematic liquid crystals in the isotropic state, appropriately modified to reflect the activity of bacteria. We show, in particular, that the non-equilibrium contributions to the stress arising from the swimming of the bacteria lead to a $1/sqrt{omega}$ scaling in the power spectrum of the active stress fluctuations, as observed experimentally.