Thousands of homes in Northern Ireland remain without power after Storm Isha caused severe disruption.
The Police Service of Northern Ireland (PSNI) said a number of roads across Northern Ireland remain impassable on Monday.
It said between 15:30 GMT on Sunday and 02:00 on Monday officers dealt with about 600 calls related to the storm.
NIE Networks said about 24,000 customers were without electricity.
In the Republic of Ireland, about 155,000 homes and businesses are without power.
A further spell of very windy weather could bring further disruption this week as Storm Jocelyn approaches from the Atlantic, BBC News NI weather presenter Barra Best said.
The storm has been named after Dame Jocelyn Bell Burnell, a leading astrophysicist from Northern Ireland, by Irish weather service Met Éireann.
There will be a yellow warning for Northern Ireland from 16:00 on Tuesday.
The wind alert will stay in place until 13:00 on Wednesday after which the winds should begin to ease.
Although not expected to be as severe as Storm Isha, the Met Office is warning of wind gusts up to 65mph, possibly stronger in more exposed locations.
On Monday, PSNI Ch Supt Davy Beck said there is “a continued risk of significant debris on the road network” and he urged “extreme caution” for road users.
Colin Sykes, from the Department for Infrastructure, said it had been a “very difficult evening” with over 1,000 incidents to deal with.
“Of that 930 were reports of trees and branches down across roads, so it is widespread disruption right across the road network,” he told BBC News NI.
He said ongoing industrial action had “disrupted our ability to provide services”.
“However, last night, given how dangerous the conditions were becoming, it was becoming increasingly difficult for us to be able to respond on the roads,” he continued.
Mr Sykes said the department had contingency plans in place including diverting other staff and using private contractors.
This means the response will be “slower”, but, he added: “We will start to work through all of the priority routes and start to unblock as much as we can.”
The managing director of Belfast International Airport, Graham Keddie, said Sunday was “tough” for its teams, but most aircraft had landed and they had returned to “virtually normal operations” on Monday.
Translink said a tree had fallen on the Lisburn train line, causing delays and disruption to the Portadown to Bangor rail line.
It added that due to exceptional weather all train lines are disrupted on Monday morning. Travel updates are available here.
In County Londonderry, the PSNI said the Ballyquinn Road near Dungiven and Seacoast Road, Limavady, were closed to traffic due to fallen trees in the area causing an obstruction.
The PSNI said a multi-agency response continues to deal with the aftermath and recovery from Storm Isha and thanked the public for their “continued patience and understanding”.
A number of schools are closed on Monday. They are Nettlefield PS in Belfast, St Mary’s PS in County Tyrone, and County Down schools Killinchy PS and Meadow Bridge PS.
The Department of Agriculture Environment and Rural Affairs said Peatlands Park and Crawfordsburn Country Park are closed due to fallen trees. It added that car parking facilities and paths have been “impacted at Roe Valley Country Park, Ness Country Park and Banagher National Nature Reserve”.
A yellow weather warning for high winds ended at noon on Monday after an earlier amber warning.
A status yellow warning remains in place for six counties in the Republic of Ireland until 19:00 on Monday.
Analysis: BBC News NI weather presenter Angie Phillips
It was the north, the west, as well as Killowen in County Down in the south-east that bore the brunt of the high winds.
The peak of the winds from Storm Isha occurred on Sunday evening; 80mph at Magilligan, County Londonderry 79mph at Castlederg, County Tyrone, 76mph at Killowen, County Down.
The peak of the winds has passed, but we still have a yellow warning for winds in place for Monday, currently for the morning, but I have a feeling this warning will be extended.
We could still see gusts of 50-60mph towards the north coast later on Monday, elsewhere perhaps 40-50mph, so there is still potential for disruption.
Claire Scullion, from NIE Networks, said at its peak 53,000 customers were without power.
“The force of the gusts and the sustained nature over several hours caused significant damage and the flying debris,” she told BBC News NI’s Good Morning Ulster programme.
“The fallen trees and the weather conditions made repairs very difficult over the night. We would say to the public, please do not approach any broken poles, overhead lines or any damaged electrical equipment.”
NIE Networks said the worst affected areas are Dungannon, Downpatrick, Enniskillen, Newry and Omagh, but added that there “are faults throughout Northern Ireland”.
Power outages or any incidents of damage to the electricity network can be reported to the NIE Networks Customer Helpline on 03457 643 643.
The disruption has affected thousands of air passengers across the UK and Ireland.
Among the flights diverted from Belfast International Airport on Sunday was a plane from Bulgaria carrying a group including 19 pupils and three teachers from Mill Strand Integrated Primary School in Portrush.
Principal Philip Reid said they experienced “extreme turbulence” as the plane made two attempts to land before being diverted to Manchester.
In Belfast city centre on Sunday afternoon, police advised pedestrians to avoid the Castle Lane area.
Officers closed Castle Lane at its junction with Royal Avenue after a member of the public was struck by falling debris, requiring hospital treatment.