A Status Orange wind warning for counties Donegal, Leitrim and Sligo has just come into place, and will be in place until 8am.
Met Éireann said it could cause further damage to already weakened structures, lead to fallen trees, damage power lines and cause possible power outages.
It will also cause very difficult travelling conditions and possible wave overtopping.
A Status Yellow rain warning is also in place for Donegal, Leitrim and Sligo.
Though the worst of Storm Amy has now passed, Met Éireann Status Yellow wind warnings are still in effect for counties Clare, Kerry, Galway, Mayo, Louth, Dublin and Wicklow.
They will be in place until noon.
Similar advisories apply to Northern Ireland until midnight.
ESB Networks crews will begin recommencing efforts to restore electricity to over 120,000 customers who have lost power as a result of Storm Amy.
There are pockets of power outages in most parts of the country this morning, but the impact is being felt most in Connacht and in the border counties.
ESB networks personnel, backed up by partner contractors, are being deployed to assess the damage and restore supply.
The company says it will update estimated restoration times on its powercheck.ie website.
People are being advised to report any issues and to stay well clear of any fallen trees or poles, which could be concealing live wires.
The storm also brought localised flooding, fallen trees, transport disruption and school closures.