The Equatorial lonization Anomaly (EIA) development can undergo drastic modification in the form of an anomalous occurrence at local times outside that of its quiet time development and/or inhibition/enhancement at local times of its normal occurrences. This happens for disturbed electrodynamic conditions of the global ionosphere-thermosphere-magnetosphere system, consequent upon the triggering of a magnetospheric storm event. Direct penetration to equatorial latitudes of the magnetospheric electric fields and the thermospheric disturbances involving winds, electric fields and composition changes produce significant alteration in the EIA morphology and dynamics. Results on statistical behaviour based on accumulated ground-based data sets, and those from recent theoretical modelling efforts and from satellite and ground-based observations, are reviewed. Some outstanding problems of the EIA response to magnetospheric disturbances that deserve attention in the coming years are pointed out.