Update - 12.28pm: Luas services will not resume on the Red and Green Lines today after yesterday's storm.
The transport operator have said that Ophelia damaged the roof on their Red Cow depot yesterday at around 2.30pm, and the firm contracted to repair the roof have estimated it will take the whole day.
The damaged section of roof is over their technical rooms which house the systems that look after overhead power and the automatic vehicle location system.
Luas services will resume tomorrow morning at 5.30am.
Update - 10.05am: The Luas is out of action after its Red Cow depot was damaged in the storm.
That means there are no trams on the Red or Green lines this morning but Transdev's Dervla Brophy says they could be back later.
She said: "So we'll be having as meeting today at 12 o'clock and then we'll be in a position to update our customers and the public in relation to what the service will be later this afternoon."
Earlier: Public transport is starting to return to normal, with the exception of Dublin’s Luas which will not be operating this morning.
Schools remain shut today, but universities and third level institutions are starting to reopen.
However, some train services are suffering delays this morning.
06:10 Waterford Heuston running approx 60mins late due to debris on the line— Iarnród Éireann #StaySafeSaveLives #HoldFirm (@IrishRail) October 17, 2017
Barry Kenny of Irish Rail said: "We do have a full service today with some minor exceptions. The 5.50 from Cork to Dublin was cancelled and the 9.45am from Westport to Dublin was cancelled as well.
"The Limerick to Ballybrophy via Nenagh service will be replaced by bus transfers.
"I should warn that there are some delays of between 15 and 25 minutes as the last debris is cleared."
All lines open except Nenagh branch. Some delays due to debris being cleared & low rail adhesion. Full info: https://t.co/ZOHwurtrN3 pic.twitter.com/CNQclfqDpd— Iarnród Éireann #StaySafeSaveLives #HoldFirm (@IrishRail) October 17, 2017
Bus Eireann have said that the majority of their services are operating this morning, except for the following services.
The bus operator said that there are some delays in the Northwest of the country due to the road conditions, while routes 215, 223 and 233 in Cork are experiencing disruptions due to fallen trees.
In Galway, route 401 has been diverted due to the closure of Salthill promenade.
Dublin Bus is back up and running following Ophelia.
Spokesperson Maria Payne says there are some minor diversions due to debris on roads.
She said: "Buses are operating as normal this morning. We have some very minor diversions due to some roads which are still blocked at the moment.
"These affects route 39 in Blanchardstown, routes 7d, 59 and 111 in Dalkey and route 66 in Leixlip."
DARTs are back on track in Dublin although there may be delays where crews continue to clear debris.
Barry Kenny said: "Well thankfully, thanks to our crews working across the network overnight removing trees and other debris, we do have a virtually full service today.
"All DART and commuter services are operating fully."