The paper traces the development of a global approach to the electric activity of the brain, from its roots in non-linear dynamical approach to the current state of art. The rationale of a three-dimensional system of global multichannel EEG descriptors (sigma, phi and omega) is provided and results obtained by means of the global descriptors in various application areas are summarised. Finally, arguments in favour of a global, 'holistic' assessment of brain functional states are presented. Definitions and properties of the global EEG descriptors are summarised in the Appendix.