Neuronal avalanches are spatiotemporal patterns of neuronal activity that occur spontaneously in superficial layers of the mammalian cortex under various experimental conditions. These patterns reflect fast propagation of local synchrony, display a rich spatiotemporal diversity and recur over several hours. The statistical organization of pattern sizes is invariant to the choice of spatial scale, demonstrating that the functional linking of cortical sites into avalanches occurs on all spatial scales with a fractal organization. These features suggest an underlying network of neuronal interactions that balances diverse representations with predictable recurrence, similar to what has been theorized for cell assembly formation. We propose that avalanches reflect the transient formation of cell assemblies in the cortex and discuss various models that provide mechanistic insights into the underlying dynamics, suggesting that they arise in a critical regime.