Passive soft materials, even complex ones, display mechanics which can be largely understood in terms of temperature. It is tempting to apply these concepts to biology, however, biological systems are far from equilibrium. Indeed, biological systems are unique among materials in that they not only produce active forces, but they also dynamically change their mechanical properties; both of these are essential aspects of animal life, and they function together to create surprising properties. In this talk, I will present some of our recent findings on how active processes can produce random "diffusive-like" transport in the cytoplasm of living cells. Using a combination of particle tracking and active microrheology, we quantitatively determine the contribution of active ATP driven-processes, and show that these dominate random transport activity on time-scales greater than about 1 second.