The ESB has said that 2,000 homes in the Cavan/Monaghan area may remain without power until tomorrow morning.
However, emergency crews have returned power to 58,000 customers following damage caused to lines in last night's storm.
Some roads have been blocked by fallen trees, and heavy rain and coastal flooding have also caused problems.
Gardaí are continuing to urge motorists to avoid any unnecessary journeys and to drive with extreme care. Many roads remained closed for much of today.
In the North, trees blocked a number of roads following last nights storm and motorists were also advised to drive with caution.
There was also flooding in some areas.
At one stage 73,000 homes were without power supplies but Northern Ireland Electricity say the number has now been reduced to 20,000 customers.
The worst affected areas are in Co Down and Co Armagh including Downpatrick, Newry and Craigavon.