ESB Networks say they have restored electricity to 20,000 customers who lost power due to Storm Barney.
Currently 25,000 customers remain without power.
The southern half of the country is worst affected as the storm crosses the country with gale force winds with gusts of up to 125 kilometres per hour.
The areas worst affected include Portlaoise, Kilkenny, Ennis, Athlone, Naas, Wicklow, North Wexford, Tullamore, Mullingar and Celbridge.
Blustery conditions will continue tonight, with winds of up to 80 kilometres an hour and damaging gusts of up to 130 kilometres an hour.
A number of flights have also been cancelled or diverted at Dublin, Cork and Shannon Airports.
Passengers are advised to contact their airline for more information.
Motorists are advised to take care as there are reports of debris on many roads.
Tullamore, Athone, Ennis, Tralee, Limerick, Killarney, Newcastlewest, Killkenny, Clonmel, Roscrea and Bray are all affected by the power outages.
The ESB says crews have been dispatched in the affected areas to assess the damage, and restore power as quickly as possible.
It says further damage and loss of electricity supply is expected.
Two national weather warnings are in place across the country.
This is the second storm of the season, following on from Abigail last week.
There is an orange wind warning for Munster, Leinster, Galway and Roscommon.
Dublin Airport says the strong winds are "likely to impact the flight schedule".
While Cork Airport says a number of flights have been cancelled due to the high winds.
Cityjet, Flybe and Aer Lingus have all cancelled services.
The UK Met Office has also issued several warnings for the storm, warning of 80mph winds in exposed western areas.
British meteorologist Mark Wilson takes a closer look:
Meteorologist Mark takes a closer look at #StormBarney https://t.co/ljVAGXoeTY
— Met Office (@metoffice) November 16, 2015