Around 20,000 homes are still without power following heavy winds overnight.
ESB emergency crews have restored power to around 40,000 homes which were affected by stormy conditions, with the east coast and the midlands the worst affected areas.
Met Eireann has issued a severe weather warning across the country, with storm-force winds expected on all coastal areas over the weekend.
Parts of Galway and Limerick were affected by flooding, and flooding also forced the Dublin to Tralee train service to end at Killarney where buses were laid on to take people the rest of their journey.
Gardaí have urged motorists to avoid any unnecessary journeys as wet and windy conditions continue.
AA Roadwatch has reported that there are fallen trees on secondary roads around Dundalk.
The clear-up in other parts of the country has continued during the day and many of those roads which had been closed earlier have been re-opened. However motorists are being urged to drive with extreme caution in Co Galway where some secondary roads remain blocked due to fallen debris. There is also spot flooding and surface water reported in some areas.
Police in Northern Ireland said roads in Omagh, Newry, Portadown and Carrickfergus were also badly affected by the storms.
A PSNI spokeswoman said there were reports of trees down on roads across the North, while power lines were also affected in some areas. She said three people were taken to hospital when a tree fell on their car on the Martrey Road in Ballygawley, Co Tyrone.
A chimney also collapsed on parked cars in India Street, south Belfast.
The PSNI has warned drivers that high-sided vehicles including lorries and buses would be unable to exit Newcastle in Co Down due to fallen trees. The River Road in Dunmurry, south Belfast, was also closed due to a fallen tree.
A spokesman for the Northern Ireland Roads Service said it would take some considerable time to reopen all the affected roads.
Additional reporting PA