Extreme geomagnetic storms are considered as one of the major natural hazards for technology-dependent society. Geomagnetic field disturbances can disrupt the operation of critical infrastructures relying on space-based assets, and can also result in terrestrial effects, such as the Quebec electrical disruption in 1989. Forecasting potential hazards is a matter of high priority, but considering large flares as the only criterion for early-warning systems has demonstrated to release a large amount of false alarms and misses. Moreover, the quantification of the severity of the geomagnetic disturbance at the terrestrial surface using indices as Dst cannot be considered as the best approach to give account of the damage in utilities. High temporal resolution local indices come out as a possible solution to this issue, as disturbances recorded at the terrestrial surface differ largely both in latitude and longitude. The recovery phase of extreme storms presents also some peculiar features which make it different from other less intense storms. This paper goes through all these issues related to extreme storms by analysing a few events, highlighting the March 1989 storm, related to the Quebec blackout, and the October 2003 event, when several transformers burnt out in South Africa.