The highest warning levels possible have been issued by Met Éireann for all but a handful of counties - Cavan, Monaghan and Donegal are under the lesser, but still serious, amber alerts.
According to electricity provider ESB, more than 200,000 homes are expected to remain without power overnight.
"The electricity network has sustained extensive damage as a result of today's storms," Jerry O'Sullivan, Managing Director of ESB Networks, said.
"ESB Networks crews have been working throughout the day to restore power, however extremely dangerous conditions are hampering their efforts and will mean that up to 200,000 customers may be without power overnight."
We are dealing with a situation that is as bad, if not worse, than anything that we have seen in the past decade.
Winds of close to 100mph have been reported and there have even been reports of a small tornado in Co Roscommon.
The highest waves ever recorded in Irish waters have also been registered south of Cork, reaching 25 metres.
Shannon Airport was forced to close for a time after a stationary plane was blown onto its wing, but has since resumed services.
Services at Cork Airport have been suspended, while flights at other airports may also be affected and passengers should check with their airline.
Some flights were being diverted from Dublin Airport to Belfast International for a time.
All Irish Rail services to and from Cork and Kerry have been suspended.
On the roads, trucks have been blown over by the high winds and some roads have been blocked by fallen trees, telephone poles and other debris.
Residents at the Waterway Apartments block in Dublin have been evacuated due to structural damage caused by the storms.
Gardaí said: "The Ashtown road is closed to traffic and road users are requested to use River road as an alternative. Gardaí, Emergency Services and Local Authority are at scene."
University College Cork has been evacuated while the University of Limerick is in lockdown due to flying debris on campus.
In Co Clare, the County Council An Garda Siochána, the Fire Service and Clare Civil Defence are responding to more than 150 separate weather related incidents.
The southeast of the county is reportedly one of the worst affected areas, particularly in Killaloe and around Sixmilebridge.
A major emergency was declared in Co Kilkenny earlier but it has since been stood down.
The local coordination group - including gardaí and fire officers - has been meeting in response to the situation and will remain in place to monitor developments until 10pm.
A statement said all urban roads are now open, but some local ones are still affected by fallen trees and other debris, and motorists are being advised to exercise caution.
It added: "Members of the public should be acutely aware that trees which have fallen may pose and additional danger because of entangled live electrical cables."
The area surrounding Nolan Park remains closed due to damage to the roof.
Major emergency plans are only put in place when there is a risk of death or serious injury, serious disruption to essential services or serious damage to property, the environment or infrastructure.
While the high winds are expected to ease overnight, Thursday looks set to bring further snow and rain for parts of the Republic and Friday will likely see very heavy rain in Cork, Waterford and Wexford.