High winds and rain were worst in Cork, Kildare and Wicklow
The ESB is advising any homeowners without power over the Christmas period to report it.
Many customers were left without power overnight - following a number of outages - as a result of Storm Eva.
ESB crews have been working throughout the day to restore power to all customers - 2-thousand people in Killibeg are still without power.
The Communications Spokesperson with the ESB, Bernadine Maloney, has this advice for people.
The vast majority of people affected by outages following Storm Eva have had their power restored.
Around 1,000 people are still without power, but crews expect to resolve all problems this afternoon.
The ESB says a major fault on Leeson Street in Dublin city centre has been fixed - leaving just a few hundred people in Cavan and Wexford still in the dark.
High winds are still being felt in many parts of the country - but Met Éireann says the worst of the storm has passed.
High winds and heavy rain battered the country yesterday evening with counties Cork, Kildare and Wicklow worst affected.
Two wind weather warnings have also been lifted.
As many as 6,000 homes and businesses were affected by power outages overnight and early this morning.
Joan Blackburn from Met Éireann says Storm Eva brought winds of up to 130 kilometres per hour:
"The worst of the winds were up around the west and north west of the country, where they gusted between 100 and 130 kilometres per hour and even parts of the east and south winds gusted over 100 kilometres an hour."
Iain Miller of uniqueascent.ie filmed this footage of Storm Eva arriving at Crohy Head in Western Donegal: