ESB Networks has said 49,000 customers have had their electricity supply restored after outages across the country as a result of Storm Doris
Some 8,000 customers remain without a power supply.
Speaking on RTÉ's Six One, ESB Corporate Communications Manager Bernadine Maloney said she expects the majority of homes will see power restored tonight.
About 56,000 homes were affected earlier.
Large faults had been reported in counties Galway, Mayo, Sligo, Leitrim and Dublin.
Portarlington in Co Laois and Celbridge in Co Kilare also experienced large outages.
Speaking on RTÉ's Morning Ireland, Ms Maloney asked customers to check on the ESB's powercheck website to see if their outage is listed.
If it is not, customers can contact EBS Networks on 1850-372-999.
She urged everyone to be careful until power has been restored and to report any fallen lines to the ESB.
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Met Éireann had issued an orange wind warning, the second highest level, for many counties, but it has now lapsed.
Some flights from Dublin Airport have been cancelled and others face delays.
A spokesperson for Aer Lingus said early morning departures were delayed due to ground wind conditions.
Passengers are advised to check the website before departing for the airport.
Ryanair has also said some flights have been delayed.
AA Roadwatch is reporting that fallen trees on roads around the country are causing traffic disruption.
Some Iarnród Éireann services were disrupted, and delays continue.
Update: all lines now clear of trees and operating. DART, Northern Commuter delays of 5-20 mins remain but will ease. #stormdoris— Iarnród Éireann (@IrishRail) February 23, 2017
Some ferries between Ireland and the UK have also been cancelled.
Passengers are advised to check with their operator.
Woman dies after being hit by debris in UK
A woman has died after being struck by flying debris in the English city of Wolverhampton, while two others were left with serious head injuries in separate incidents.
West Midlands Police confirmed the 29-year-old woman was "struck" by "wooden debris from a nearby building" and have said they are working with Wolverhampton Council to establish how the incident happened.
The weather system, which brought gales, snow and rain to much of the UK, also caused travel disruption on the roads and rail network, brought down trees, grounded planes, and toppled large vehicles.