Although the extracellular space in the neuropil of the brain is an important channel for volume communication between cells and has other important functions, its morphology on the micron scale has not been analyzed quantitatively owing to experimental limitations. We used manual and computational techniques to reconstruct the 3D geometry of 180 μm3 of rat CA1 hippocampal neuropil from serial electron microscopy and corrected for tissue shrinkage to reflect the in vivo state. The reconstruction revealed an interconnected network of 40–80 nm diameter tunnels, formed at the junction of three or more cellular processes, spanned by sheets between pairs of cell surfaces with 10–40 nm width. The tunnels tended to occur around synapses and axons, and the sheets were enriched around astrocytes. Monte Carlo simulations of diffusion within the reconstructed neuropil demonstrate that the rate of diffusion of neurotransmitter and other small molecules was slower in sheets than in tunnels. Thus, the non-uniformity found in the extracellular space may have specialized functions for signaling (sheets) and volume transmission (tunnels). J. Comp. Neurol. 521:448–464, 2013. © 2012 Wiley Periodicals, Inc.