Forecasters say blustery conditions and showers will continue well into this afternoon.
Orange wind alerts are in place for Donegal, Leitrim, Mayo and Sligo, with yellow alerts for Munster, Leinster, Cavan, Monaghan, Galway and Roscommon.
There is a lot of debris on roads this morning and drivers are asked to take extra care.
The conditions are as a result of the country being hit by the tail end of Hurricane Gonzalo, which has severely damaged buildings and caused powercuts in Bermuda.
Met Éireann forecaster John Eagleton said: "The winds will be strongest in the north west. It will be very windy until about midday, and it will ease down in the afternoon and evening."
Meteorologist with Met Éireann Jean Byrne said the worst gusts so far - of 110kms per hour - were recorded in Malin Head around midnight.
The gusts are between 85kms per hour and 95 kms per hour in many other parts of the country, she said.
Ferries and flights hit:
Irish Ferries has had to cancel a number of its Jonathan Swift vessel's sailings today because of the weather conditions.
Services from Dublin at 8.45am and 2.30pm are cancelled, as are the services from Holyhead at 11.50am and 5.15pm.
Passengers will be accommodated on the Ulysses cruise ferry.
The Ulysses morning service is also running behind schedule due to bad weather on the Irish Sea this morning.
It is now due to arrive in Dublin at 7.30am.
The poor conditions have hit flight schedules too.
London Heathrow said that about 10% of their services would be disrupted by the high winds.
Intending passengers have been asked to check with their airlines for latest updates.
Aer Lingus said yesterday that four flights on their service between Dublin and Heathrow had been cancelled today.
A number of Dart and rail services around Dublin have also been disrupted by fallen trees.