The highest-level red warning was in effect in County Donegal from 16:00 (local time) until it was downgraded to orange from 18:00, which has been issued until 22:00.
Malin Head in County Donegal, the most northerly point of the island of Ireland, saw wind speeds up to 92mph.
Elsewhere, Belmullet in County Mayo and Mace Head in County Galway experienced speeds of 76mph.
The Electricity Supply Board (ESB) has said its crews are working to restore power to 124,000 homes, farms and businesses, mostly in counties  Donegal, Galway, Mayo, Sligo, Roscommon, Leitrim and Cavan.
As of 20:00 local time, a total of 115 flights had been cancelled at Dublin Airport, while 18 inbound flights were diverted to other airports.