Weather warnings remain in place today with motorists told to be particularly careful of frost and black ice this morning.
Met Éireann said cold weather was set to continue throughout the week, with low daytime temperatures and patches of freezing fog expected to make driving conditions difficult.
While some showers are expected, the weather forecaster said most of the heavy rainfall had moved off.
The Garda said there was severe flooding on nearly all routes into the capital yesterday morning, with a number of areas impassable.
Dart services were suspended through Sandycove for a time, and parts of the M1 south of Donabate saw flooding and a number of crashes.
There was severe flooding along Dublin city’s northern fringe. The road from Ballyboughal to Oldtown was impassable, as was the Old Portmarnock Road at the trotting track between Malahide and Portmarnock.
The Ashbourne/Swords road was flooded at Kells Country Club. There was also surface water at Chapelizod Road and at a number of points between there and Aylmer Road in Newcastle, Co Dublin.
Parts of Wicklow along the N/M11 were badly affected, as were parts of Wexford and some areas of Munster.
While conditions improved by yesterday afternoon, gardaí warned the freezing weather expected last night could make road conditions particularly hazardous.
The weather is expected to be mainly dry and bright today except for some coastal showers driven onshore by northerly breezes.
Patches of freezing fog will develop today and linger during tomorrow night and Thursday. Some light rain or sleet will develop in the west during Friday.
There is a gradual return to milder weather next weekend as temperatures climb towards more normal values of 9 or 10 degrees.
In the UK, where rainfall is expected to continue in many areas today, the Environment Agency has predicted river levels will swell further, with the river Severn of particular concern.
Tewkesbury in Gloucestershire is said to be particularly vulnerable, with the Severn expected to peak at 4.8m – a metre less than the 2007 peak .