The ESB say they are working to restore power to thousands of homes and businesses as Storm Lorenzo passes over the country.
However service has been restored to some 12,000 customers.
People can check the status of their area on the ESB PowerCheck website.
The network says gale force winds from Storm Lorenzo, with gusts of over 100 km/h overnight, caused damage.
This is mainly because of fallen trees on overhead lines.
The counties most affected include Longford, Mayo and Galway.
Meanwhile all previous weather warnings associated with the storm have ended.
Lorenzo has moved north-north-eastward parallel to the west coast of Ireland.
The depression took a turn eastwards while weakening.
However there could be a prolonged period of heavy rain in north-western parts of the country.
Road users are being urged to pay particular attention to the risk posed by fallen trees and flying debris, as trees are in full leaf.
See a full forecast here
In terms of outlook, Saturday will start out mainly dry and cloudy with outbreaks of rain developing by the end of the morning.
The rain will turn heavy with the risk of spot flooding and will clear in the early evening.
There will be yet another spell of rain arriving Sunday night from the west, but Sunday itself will be a dry day with mist clearing early and sunshine developing in light winds.
The rain will be heavy and bring more spot flooding.
Monday rain in the morning in the east will slowly clear and then it will be a mainly dry day with showers, mainly affecting the Connacht and Ulster.
While Tuesday and Wednesday will be similar days with fresh, occasionally strong, southwest winds with showers mostly confined to western coastal areas.
#StormLorenzo will bring rain for many areas through tonight and tomorrow - but what happens then?
— Met Office (@metoffice) October 3, 2019