All substances exhibit constant random motion at the microscopic scale. This is a direct consequence of thermal agitation, and leads to diffusion of molecules and small particles in a liquid. In addition to this nondirected motion, living cells also use active transport mechanisms, such as motor activity and polymerization forces that depend on linear biopolymers and are therefore fundamentally directed in nature. Nevertheless, it has become increasingly clear that such active processes can also drive significant random fluctuations that can appear surprisingly like thermal diffusion of particles, but faster. Here, we discuss recent progress in quantifying this behavior and identifying its origins and consequences. We suggest that it represents an important and biologically tunable mechanism for transport in living cells. © 2009 Elsevier Ltd. All rights reserved.