The weather has affected flights and ferry sailings
Met Éireann has cancelled two weather warnings after Storm Doris hit Irish shores overnight.
However a status orange marine gale warning remains in effect.
40,000 ESB customers have had their electricity supply restored, but the company added that many in the worst impacted areas will be without power overnight.
In a statement, the ESB said 17,000 electricity customers are currently without power due to over 1,000 separate faults, which will reduce in the coming hours.
The areas currently affected include:
Crews will be out again from early tomorrow morning to continue the work of repairing the network and restoring power to all customers.
Details of power outages can be found on the ESB's Powercheck website.
Damage has been caused to electricity lines by high winds - as well as damage to poles and other equipment.
The ESB says falling timber has also caused "considerable damage" to the electricity network.
ESB Networks have mobilised crews across the country who are working to restore power as quickly as possible.
Bernadine Maloney is corporate communications manager with the ESB.
Aer Lingus say Storm Doris has caused "significant disruption" to its flight schedule - including some lengthy delays and cancellations.
Travelers are advised to check with their airline before going to the airport.
While Irish Ferries say several sailings have been cancelled or delayed. These include the Epsilon and Swift services to Dublin - Holyhead.
On the roads, the AA says continued care is advised across the country.
It says while many earlier fallen trees have been dealt with, road users should keep in mind that debris may be an issue on secondary routes.
While the worst of the storm appears to have passed, windy weather is forecast with strong and gusty northwest winds.
There will be sunshine and squally showers too, a few wintry across the north and northeast.
Winds will continue to ease through the day, but remaining blustery even into this evening.
Showers will become scattered and it will be driest across southern counties.
Tonight will be cold, with an added wind chill effect and lowest temperatures of 0 to 5 degrees.