A number of homes and businesses were left without power as Storm Gareth tracked across the country, with the northwest the hardest hit.
There are reports of fallen trees and debris on many roads.
A Status Yellow wind warning for Munster, Leinster, Cavan, Monaghan and Roscommon has been lifted.
ESB Networks say a number of customers across the northwest were left without power and crews are working to restore supply.
Almost 2,000 homes, farms and businesses experienced outages, with the majority in Donegal.
A number of trees fell in Donegal, Sligo and Leitrim, but gardaí say there are no reports of any significant damage.
Bus Éireann has said all its services are operating as normal.
Storm Gareth has moved into the North Sea, although another band of wet and windy weather is expected to arrive later tonight.
The storm, caused by a deep area of low pressure, is the third named storm this year after Storm Erik in February and Freya earlier this month.
In the UK, six crew members were airlifted from a stricken French fishing boat off Lands End in "atrocious" six metre waves and storm-force winds, the Maritime and Coastguard Agency (MCA) has said.
The coastguard was alerted at around 10pm last night the fishing vessel La Fanette had suffered engine failure.
Another fishing vessel went to help and a lifeboat was launched.
"Despite atrocious weather, Sennen Cove Lifeboat launched but due to 5-6 metre waves on scene and storm force winds, it was impossible for either the fishing vessel or the lifeboat to establish a tow with La Fanette," the MCA said.
"The six crew on board were airlifted from the fishing vessel by Newquay Coastguard Rescue Helicopter."
Reporting: Eileen Magnier, PA