About 7,000 thousand homes were left without power for a time in the south of the country, after lightning damaged power lines.
ESB crews have been working since this morning on the problem.
A company spokesman said power has now been restored to about 3,500 of the homes affected, but a further 3,500 are still cut off.
Areas affected include Bandon, Co Cork and Shillelagh, Co Wicklow.
Elsewhere, gardai have issued warnings to motorists in some areas about the adverse weather conditions.
Irish Ferries announced the cancellation of all Swift sailings because of adverse weather.