Ireland's national weather service says the country has seen 114 mph wind gusts, the highest ever recorded on the island.
A red weather warning is in place for Scotland, where a "once in a generation storm" is causing widespread disruption.
ESB Networks in Ireland and NIE Networks say they expect significant further outages as Storm Eowyn continues to batter parts of the island.
A red wind warning has been issued for the whole of the Republic of Ireland, with Met Éireann warning of a possible "danger to life". The alert comes into effect at varying times from 02:00 on Friday and will end at varying times. Met Éireann has warned that "severe, damaging and destructive winds" are expected, with gusts of up to 130km/h.
There are warnings of danger to life, fallen electric lines, damaged infrastructure and widespread power outages
Storm Éowyn is slowly making its way across the UK, where its heavy winds have been hitting homes and commercial properties. In Northumberland, one bungalow had its roof torn off, while Bangor leisure centre in Northern Ireland - which is under a red wind warning - also suffered damage.
Met Éireann forecasts extremely destructive gusts in excess of 130km/h with many schools and workplaces set to close
Micheál Martin became Ireland’s taoiseach (prime minister) for the second time in his political career on Thursday, a day later than planned.
Irish lawmakers have voted to make veteran politician Micheál Martin prime minister for a second time, leading a coalition government
AN urgent warning has been issued as AIB and Bank of Ireland will shut tomorrow due to “dangerous” Storm Eowyn. A number of services will close as the entire country will be placed
Millions of people have been urged to stay at home on Friday as Storm Éowyn is set to bring potentially life-threatening winds to the north and west of the UK.
Flights and trains have been cancelled and red weather warnings are in place in Scotland and Northern Ireland as Storm Eowyn hits the UK.