Ophelia, the largest hurricane ever recorded so far east in the Atlantic Ocean and the furthest north since 1939, was downgraded to a storm before it hit the Irish coast but nonetheless posed enough of a threat for the Met Eireann national weather service to issue a red alert.
"Ex-hurricane Ophelia is forecast to track directly over Ireland," the service said.
"Violent and destructive gusts are forecast with all areas at risk."
It warned that "heavy rain and storm surges along some coasts will result in flooding. There is a danger to life and property".
Wind speeds hit 176 kilometres (109 miles) per hour at Fastnet Rock, Ireland's most southerly point, while the fastest speeds recorded onshore were 156 kph (97 mph) at the entrance to Cork Harbour in the southwest.
Dublin Airport scrapped around 130 flights; Cork Airport cancelled most flights in what it said was the worst storm seen in its 56-year history, while several services to and from Shannon, the third-biggest airport, were also grounded.
Speed restrictions were placed on trains, and some lines in the south were cancelled.
- PM says stay indoors -
"Stay indoors wherever you are until the storm has passed. Check on your neighbours and elderly relatives," Prime Minister Leo Varadkar told reporters.
"It is coming your way and this is a national red alert.
"Even after the storm has passed there will still be dangers. There will be trees on the ground and power lines down."
The education ministry said "all schools, colleges and other education institutions" were closed on Monday, after official advice on the "unprecedented storm".
Government offices were also closed across the country.
The military has been deployed to areas forecast to be worst affected and are on standby.
The eye of the storm is forecast to track across Northern Ireland and then Scotland.
Though it will weaken as it goes, gusts are expected to reach 80 mph (129 kph) in the UK.
Britain's Met Office issued amber warnings for Northern Ireland, Wales, and southern Scotland.
"There is a good chance that power cuts may occur, with the potential to affect other services, such as mobile phone coverage," the UK national weather service said, warning of transport disruption.
"Flying debris is likely, such as tiles blown from roofs, as well as large waves around coastal districts with beach material being thrown onto coastal roads, sea fronts and properties.
"This leads to the potential for injuries and danger to life."
The storm came 30 years to the day of the Great Storm, which ravaged southern England in the early hours of October 16, 1987, leaving 18 people dead.
- Hurricane season -
Ophelia is the 15th named storm of the 2017 Atlantic season, which is expected to last until the end of November.
Three major hurricanes -- Harvey, Irma and Maria -- caused catastrophic damage in the Caribbean and the US Gulf Coast.
Meteorologists say Ophelia was the most powerful hurricane recorded so far east in the Atlantic and the first since 1939 to travel so far north.
It was classed Category 3 on Saturday as it passed near Portugal's Azores islands, which means it packed winds of at least 178 kilometres (110 miles) per hour.
Seven of the nine islands in the Azores were put on high alert for the storm's passage, but it did not cause major damage, authorities told reporters.
In Spain, three people have died in wildfires whipped by strong wind gusts spawned by Hurricane Ophelia.
Six people have also died in wildfires in Portugal, which local authorities said had been exacerbated by drought.