The president is Ireland’s “first citizen”, but has limited power – the role is mainly symbolic and he or she cannot get involved in daily politics.
Voters are also being asked whether they want to remove the offence of “blasphemy” from the constitution.
Many were unaware there was such an offence until referred controversial remarks made by the actor and writer Stephen Fry on an RTE programme about what he regarded as God’s cruelty to the police force, the Garda Siochana.
But the matter was dropped when gardai (police officers) could find no-one who was offended.
The last person to be prosecuted for blasphemy was in 1855 when the British ruled Ireland.
In the presidential poll, Mr Higgins’ rivals include:
Liadh Ni Riada, the Sinn Féin MEP
Senator Joan Freeman, a campaigner on mental health issues and the founder of the charity Pieta House
Sean Gallagher, a businessman who was the runner-up seven years ago
Gavin Duffy, a former broadcaster who now works as a businessman in the communications industry
Peter Casey, a Londonderry-born businessman and who made his fortune abroad
The three businessmen were all “dragons” in the Irish version of the Dragons’ Den TV programme.
Dublin Castle announcement
Polls suggest that people will vote overwhelmingly to remove references to the offence from the constitution.
The measure has the support of all the main parties and the main Christian churches.
People living on islands off the coast of Donegal, Mayo and Galway have already voted in the presidential election and referendum on blasphemy to guarantee that weather conditions would not prevent their ballots being counted with the rest of the country.
Polls will be open from 07:00 local time until 22:00.
Counting in centres across the state will begin on Saturday morning at 09:00.
The official result, expected on Saturday evening, will be announced at Dublin castle.