The northwest and Connacht were recovering yesterday after hurricane force winds gusted to 174 kilometres an hour.
The speeds, recorded at Malin Head on Tuesday night, were the third highest in the area since records began.
Up to 20,000 homes were without power following the storm and 8,500 Eircom customers were without phone lines. Black ice, snow, flooding and debris made some roads impassable.
The centre of Tuesday's storm passed within 130 km of the northwest coast.
With mean wind speeds of 117km/h at Malin Head and 174km gusts, the storm was powerful enough to be classified as hurricane force.
Belmullet in Co Mayo also experienced high winds, with gusts of 133km/h.
A spokesman for the ESB said they hoped to have power restored to 20,000 homes around the country by late last night. The bulk of the damage was done to power lines in the northwest after 11pm on Tuesday, he said, when the high winds brought lines down or caused trees to fuse them.
However, homes on the Cork and Kerry coast also lost power when transformers were hit by lightning at lunchtime on Tuesday.
The spokesman added that repair crews were able to get to the faults quickly because they had been on standby after a severe weather warning was issued by Met Éireann on Tuesday morning.
He also said that power lines had been strengthened over the last five years and this had helped to reduce the potential for damage.
A spokeswoman for Eircom said it had put in place a storm recovery plan after 8,500 telephone faults were reported around the country.
The worst-hit areas included parts of the northwest, southwest, Connacht, Carlow, Kilkenny and Tipperary.
The company's call centres continued to receive complaints yesterday and, the spokeswoman said, all emergency crews had been deployed and staff from other areas of the business were redirected to assist the repair teams.
"We estimate at this stage that it could be the middle of next week before service can be restored to some customers," she added.
According to Met Éireann, gales, with wind speeds over 62km/h, are experienced on average more than 50 days each year at northern coastal locations, making the north and west coasts of Ireland two of the windiest areas in Europe.
By comparison, Kilkenny experiences an average of only two days with gales every year.
