Here we summarize the main arguments proposed in the present work for the interpretation of spatio-temporal neurodynamics as large-scale phase transitions over the cortex. Experimental data indicate that the necessary macroscopic frames with beta-gamma carrier frequencies are readily found in human volunteers engaged in cognitive tasks. Our theoretical results show that brains have a efficient mechanism to generate the conditions for very rapid switches and reduce the waiting time between the transitions, as observed in EEG/ECoG data. We elaborate on the consequences of these findings to normal brain operation and to brain diseases.