ESB Networks has said 500 homes are still without power tonight and warned that some customers may be left without power until tomorrow.
Customers along the western seaboard are the worst affected.
Eircom said it has deployed additional crews to repair faults on its phone lines. It said it is dealing with almost 5,000 reported faults.
Last night saw winds gusting at up to 160km/h, with exposed parts of the north and northwest the worst affected.
ESB corporate communications manager Brian Montayne said the northwest remains the worst affected today, but outages also occurred in the midlands and in Co Wexford.
The severe winds have also caused widespread disruption to transport and drivers have been warned about debris on the roads, including trees and household bins.
In counties Galway and Mayo, gardaí received a number of reports of fallen trees, some of which are blocking roads.
The strong winds have also forced the delay or cancellation of a number of flights to the UK.
Passengers have been advised to contact their airline for further information.
In Cork, motorists in Fermoy have been asked not to park along the quays, as there is a possibility of some flooding at high tide tonight.
