Understanding complex systems like brain networks is a challenge. Cortical networks can perform computations of remarkable complexity, accounting for a large variety of behaviours and cognitive states. At the same time, the same networks can engage in stereotypical patterns of spatio-temporal activation, such as the ones that can be observed during sleep, anaesthesia and in cortical slice. Collective phenomena emerging from activity reverberation in cortical circuits at different spatio-temporal scales results in a rich variety of dynamical states. Slow (around or below 1 Hz) and fast (15–100 Hz) rhythms are spontaneously generated by the cortical network and propagate or synchonize populations across the cortex. This is the case even in isolated pieces of the cortical network, or in vitro maintained cortical slices, where both slow and fast oscillations are also spontaneously generated. We understand that these emergent patterns provide information on the structure, dynamics and function of the underlying cortical network and their alterations in neurological diseases reveal the circuits dysfunction. In particular in this talk we will concentrate in cortical columnar activation and wave propagation.