Volume transmission involving the migration of chemical signals through brain extracellular space is primarily mediated by diffusion. This review summarizes the biophysical basis of diffusion in the brain and describes how tortuosity and volume fraction of the extracellular space modify the process. Recent work using both Monte Carlo simulation and experimental measurements suggests that the extracellular space may consist of both well-connected regions and dead-space microdomains. The review concludes with a brief overview of previous work on diffusion in the aging rat brain.