Met Éireann say the strongest winds at the moment are on the south coast as many areas of the country experience stormy conditions.
The ESB says crews are working flat out to restore supply to about 40,000 homes.
Areas affected include Wexford, Kildare, Longford, Mullingar in Co Westmeath and north Dublin. Parts of Bray in Co Wicklow and Shankill in south Dublin are also affected.
The outages have been caused mainly by falling timber on power lines, a spokesperson for the company said.
The DART is now suspended between Dún Laoghaire and Bray for the rest of tonight.
Iarnród Éireann says they are working to clear fallen trees and branches from the line and hope to have services restored by the morning. Dublin Bus is honouring DART ticket holders.
The LUAS Red Line has also been cancelled because of fallen overhead cables.
Gardaí in Co Kildare say a number of roads across the county have been blocked by fallen trees and they advise motorists not to travel.
High winds have blown down trees in a number of places in Co Galway.
Fire service personnel are attempting to remove a tree which has fallen on the Portumna to Birr road and a tree is partially blocking the Galway to Barna road.
Severe flooding in Cavan and Monaghan
Severe flooding occurred in parts of counties Monaghan and Cavan as a result of heavy rainfall yesterday evening.
A number of premises near Castleblayney were affected and three fire brigade units were called to pump out flood water.
More serious flooding was reported in the Clones and Ballybay areas of Co Monaghan.
Many areas of farmland were under water this morning.
Floods were also reported in low-lying areas near Cootehill and Shercock in Co Cavan.
