Met Éireann has issued a severe weather warning as up to 70,000 homes are without electricity and fallen trees and telegraph poles have made some roads impassable around the country.
The west coast has been particularly badly hit and AA Roadwatch has advised motorists to drive with extreme care and watch out for fallen debris.
A spokesman for the ESB said areas such as Kerry and Cork were among the first to be affected by fallen power lines, but that parts of Sligo were now suffering power failure as winds and debris damaged overhead lines.
Flooding and fallen trees had blocked roads in areas as far apart as Waterford and Galway, while a vessel was said to be in difficulties off the Kerry coast.
Severe weather had been warned for today, but the ESB said its workers were doing their utmost, within safety limits, to restore services.
The spokesman said: "We are doing as much work as we can, as fast as we can." It is hoped power will be restored before tonight, but customers were warned that conditions may make it impossible to restore electricity supplies in all areas until tomorrow.
In Tipperary, the New M8 between Urlingford and Cullahill is closed southbound due a fallen sign and diversions are in place via Johnstown to Urlinford.
Met Éireann0 has warned of severe winds of up to 140 km/h and extensive rainfall is expected later today.
There is also a risk of flooding in parts. Power lines have come down in the west and south west. Emergency repair crews are working to restore power.
A number of flights from Dublin Airport have been cancelled and travellers are advised to check flight times with their carrier.