The Electricity Supply Board has said the storm has done 'significant damage' to the country's network.
Thousands of homes across the country will be without power overnight.
Counties affected by power outages include Dublin, Cork, Tipperary, Waterford, Cork, Louth, Clare, Kilkenny and Galway.
ESB said tonight that while crews were working to restore supply, some customers will be without power overnight.
"We are still working to restore supply but if you are not restored by midnight, it is likely that you will be without supply overnight," the company said on Twitter tonight.
Meanwhile, a massive storm surge has overwhelmed Cork’s quay walls and left parts of the city centre resembling a lake.
The one-metre surge - driven by gale force winds - resulted in a high tide swamping quay walls along Cork’s south channel and the River Lee flooded low-lying parts of the city centre.
Cork’s main retail streets including Oliver Plunkett St and South Mall were swamped at 8.15pm, almost an hour before high tide.
The floods reached almost a metre in depth in parts.
Luckily, a dramatic easing in the wind at 8.30pm helped spare Patrick Street. But a lightning strike caused a blackout on Oliver Plunkett Street.
Over 2,000 sandbags were issued by Cork City Council and a number of businesses also closed early to allow flood gates and sand-bags to be installed.
The scale of the flooding prompted the HSE to issue a health alert amid fears over the bacteria-laden waters which may contain sewerage.
It is the fourth time in just four weeks that parts of Cork city has flooded.
Desperate efforts by Cork City Council, Cork Fire Brigade, Gardai, Naval Service, Defence Forces and trader groups helped to minimise the damage.
Gardai In Cork city are currently manning junctions preventing traffic from entering the city centre. The Jack Lynch tunnel and Ring road are open and traffic is moving normally.
Lower Glanmire road is closed outbound and inbound, and Patrick Street is closed in both directions.
Deluges also hit Cork towns including Mallow, Fermoy, Youghal, Bandon, Cobh, Clonakilty, Carrigaline and Bantry.
Access to Cobh on Great Island was again restricted because of flooding by Belvelly Bridge.
Meanwhile, no further flooding has hit Limerick,. High tides over the next 36 hours are predicted to be up to two metres lower than on Saturday when the worst floods in living memory hit the city.
Gardai have warned that numerous trees have fallen around the country and people should stay indoors - unless their journey is absoloutely necessary.
The River Lee broke its banks in Cork city centre, 50 minutes before high tide and the Cork city council, gardai and emergency services were working at the scene.
Most streets in the city centre are now closed with water rising and high tide expected at 8.50pm. The Carragline road to Crosshaven is now impassable.
As county councils are braced for high tides mixed with heavy rain and high winds, gardai are warning that motorists should only venture out if their journey is essential.
Gardai have received reports of hoardings being blown from buildings. In one case in Limerick, tarpaulin blew off an articulated lorry.
In Waterford city, the quays are now closed to traffic due to flooding. Diversions are in place. A number of trees have also fallen in the area.
While in Clonmel, the Quays road has been closed due to rising water.
There have been reports of trees down in Waterford as well, gardai say.
In Wexford town, HGVs are asked to avoid the quays area and the town centre. Water has not yet breached in the area but high tide is due at 10pm and the water is rising.
While in Dublin, gardai say they are receiving many reports of fallen trees. They are warning motorists to 'be carefull driving and slow down, a fallen tree could be around the next bend'.
The Luas had to be stopped in both directions at the Marlborough Street/ Abbey Street Junction - due to debris on the line.
A tree was reported down at Church Rd, Mulhuddart at 10.30pm, blocking the road. Power lines were down.
Yet another Atlantic storm depression is approaching Ireland, bringing with it winds which could reach up to 115 kph, Met Eireann says.
Large waves, high tides and low pressure values are likely to lead to some coastal flooding.
Heavy downpours will hit and with the water table so high, river flooding is likely too, forecasters say.
Gusts of 119kph have already been recorded at Sherkin Island in West Cork this evening.
A spokesperson for Met Eireann said this evening that already - between 3pm and 6pm - there has been ten milimetres of rain.
"The rain will turn more showery and there is likely to be thundery downpours."
"The Orange warning is in place for the coastal areas of the south and the east."
Sandbags were handed out in Cork city centre to prepare homeowners and local businesses for tonight’s high tide.
In the scramble to keep their homes safe, residents used any method of transport possible to transfer the sandbags to their homes.
Cork City Civil Defence is on standby tonight to provide assistance.
Flooding is expected to hit Cork between 8pm and 10 pm tonight, with the Jack Lynch Tunnel closing from 10pm.
There were reports of strong winds and bad driving conditions in west cork in the areas of Innishannon, Crossbarry and the village of Ballinadee.
There are serious delays as a lane has been blocked on Washington Street in Cork.
A fallen tree blocked a road near a roundabout in Kinsale earlier today.
Emergency aid of €15 million is available for people who have been stricken by flood and storm damage.
Taoiseach Enda Kenny told the Dail this afternoon that this emergency fund is for immediate distress for people who have lost their homes, personal possessions, and were suffering immediate problems.
Mr Kenny said the longer-term response is being assessed and a meeting of Cabinet on Thursday will hear reports from local councils around the country about what is required to repair damage to things like roads, bridges and piers.
The Taoiseach said proposals for this longer-term aid are expected at next Tuesday's meeting of Government and added that already €250 million has also been spent on flood defences.
The Taoiseach is under pressure from the Opposition about the slow response to the damage in Limerick, Cork, Galway and other parts of the south and west.
Sinn Fein leader Gerry Adams said ordinary working people were suffering and he also said people need help to get insurance.
"Pardon the pun. But €15 million is a drop in the ocean," Mr Adams said.
Coastal regions have been warned to brace for the 'perfect' Atlantic storm which is set to make landfall over the coming days.
A leading expert has said the storm is related to global warming.
“Climate change is an important component in this. We have to remember that what we’re seeing at the moment is ratcheted up in terms of the ongoing sea level rise that we’re experiencing.
“It’s not a particularly marked rise that we’re experiencing - but even a few centimetres over previous defences can be catastrophic, as we’ve seen in Limerick”.
The unusual Atlantic storm sequence means that already struggling flood defences are being hit more regularly this winter than in previous years.
Met Eireann has said a similar storm sequence hasn’t been experienced by the country in decades.
Professor Sweeney explained: “We’re dealing with a combination of circumstances. We’ve the exceptional winter storm sequence which we’ve seen since the beginning of December, we’ve also got the juxtaposition to that of an exceptional high series of tides.
“Tides are over four meters in Dublin and Cork this afternoon and unfortunately the storms are arriving at the same time which means we’re getting a further elevation in sea levels due to the low pressure. It’s the perfect storm."
He also referred to s study his department carried out a decade ago which outlined vulnerable areas in Ireland due to rising sea levels.
“We identified 175,000 hectares which was vulnerable to sea level rise.
“We’ve more recently identified 15,000 addresses in Dublin, 12,000 in Cork, 4,000 in Limerick and 2,500 in Galway which are less than three metres above sea level.
“If you estimate from a model how much losses that would amount to you very quickly get over €1bln or €2bln. We know the costs, we know what it’s going to cost and we’ve known for some time.
He added that flood defences built in the 19th and 20th century may no longer be fit for purpose – and that the government may have to accept some areas cannot economically be protected from rising sea levels.
“We’ll have to retreat and lose some land, land which can’t be economically defended.” He said.
Ralph Riegel, Brian O'Reilly, John Downing, Aishling Phelan