The political parties were confident last night of a large turnout for today's polls.
Continuing good weather and the importance of and interest in the ballot on the Belfast Agreement are likely to yield the high turnout.
When voters enter polling stations and apply for ballot papers, they will be given two ballot sheets - a green one and a white one.
The green ballot paper is for the Amsterdam referendum.
It will ask the voter if he/she approves of "the proposal to amend the Constitution contained in the undermentioned Bill: Eighteenth Amendment of the Constitution Bill, 1998".
The Bill allows the State to ratify the treaty by amending Article 29 of the Constitution; it also allows the State to exercise options, or discretions, under certain provisions of the treaty, but only following approval by the Dail and Seanad.
Voters who approve must place an X, or other sign clearly denoting a preference, in the Yes box. Voters who disapprove should indicate in the No box. Do not write anything else on the ballot paper.
The number of people entitled to vote is 2,747,088. While possession of a polling card (each voter should by now have received one by post) is not essential - inclusion on the Electoral Register denotes an entitlement to vote - it is helpful to personation officers and should be presented when applying for a ballot paper.
If you cannot find your polling card, another form of identification such as a driving licence, medical card, cheque or credit card, or a credit union membership card will suffice. Polling stations are open from 8 a.m. until 10 p.m.
Counting takes place tomorrow from 9 a.m. in centres throughout the State based in the 41 Dail constituencies.
Counting for several of the Dublin constituencies will take place in the Industries Hall and the Main Hall of the RDS. In Cork, the North and South Central constituencies will be counted at Neptune Stadium. Cork East, North West and South West will be counted at St Finbar's Club, Togher. Counting in other constituencies will be at the usual locations.
All results will be collated at a central count, to be held in the Chester Beatty Library Building in Dublin Castle (admission by ticket only).
Counting of votes on the Belfast Agreement will take place first and it is not expected, therefore, that there will be a result of the Amsterdam referendum until mid-evening tomorrow.
The results are likely to be published first on the Irish Times website which will carry all results in full.
The full text of the Amsterdam Treaty is available on the site (http://www.irishtimes.com), which also contains the full text of the Government's White Paper as well as of the Maastricht Treaty, and The Irish Times special supplement published at the start of the campaign.