The Government has announced the terms of reference for The Commission of Investigation into Mother and Baby Homes and Certain Related Matters.
The three appointed members to head the investigation will look at the operation of 14 institutions as well as some county homes over the period from 1922 to 1998.
It will examine the pathways of single women into and out of the institutions.
The conditions and care arrangements will be reviewed.
It will also investigate burial arrangements.
The group will review whether vaccine trials were carried out on children and what arrangements for adoptions were made.
At least 23,000 babies were born in the homes being investigated.
Some survivors and their supporters watched from a separate room as Minister James Reilly laid down the Commission's parameters.
But others urged the Commission to recommend a wider trawl for illegal adoptions which did not directly implicate the homes.
Minister Reilly agreed that the Adoption Authority's recent admission that thousands may have been illegally adopted from here could lead to garda investigations.
It is understood that the authority has told the minister's department that 99 people have been illegally adopted.
But it is aware that the passage of time will make it difficult to get prosecutions.
Welcoming the Commission, historian Catherine Corless who revealed the deaths of almost 800 children at Tuam's home complained that the nuns who ran it have been less than forthcoming.
Judge Yvonne Murphy will issue a report in three year's time.
But the Minister said that in the interim, she could recommend on issues like paying redress to survivors of the Protestant Bethany Home, over 200 of whose babies were found in unmarked graves in Dublin four years ago.
Minister for Children James Reilly said the commission may produce evidence on illegal adoptions which could warrant prosecutions.
He also said it was a matter for the commission to recommend at any time over the next three years whether survivors of the Bethany Home should receive redress.
Details to be investigated
The commission will investigate the circumstances in which single women entered and left homes, the living conditions and care arrangements in the institutions, their mortality rates and burial arrangements, including anatomical experimentation.
It will also examine whether regulations were broken during vaccine trials on child residents.
Adoption arrangements, including illegal adoptions and the concealment of children's parentage will also be scrutinised.
The minister agreed that the recent admission by the Adoption Authority that thousands of illegal adoptions may have taken place in Ireland could lead to the commission informing the gardaí of such practices and to prosecutions where appropriate.
Speaking on RTÉ's News At One, he said that the issues of redress and compensation are matters for the Commission and the recommendations should be relayed to Government.
The minister said he expects full compliance, including access to Government records and that a failure to do so could result in a fine or imprisonment.
The three-person commission chaired by judge Yvonne Murphy will be given three years to complete its work.
Judge Murphy will be joined by commissioners Professor Mary Daly, a social historian, and Dr William Duncan, a family law expert.
A confidential committee that will speak to those who lived and worked in the homes will report within 18 months.
Minister Reilly said he believed the commission would be critically important in coming to terms with the country's history.
He said it will give a greater understanding of how Ireland as a society failed in its treatment of women and children in these homes.
Mixed reaction to terms of reference
The chief commissioner of the Irish Human Rights and Equality Commission, Emily Logan, has welcomed the terms of reference.
Speaking on RTÉ's News at One, Ms Logan said the terms were "very thorough" and she welcomed the fact that survivors will be able to give confidential interviews to the inquiry.
Fianna Fáil's Spokesperson on Children Robert Troy also welcomed the terms of reference, saying that it gives the Government "the scope to allow Judge Yvonne Murphy to examine any institution which she believes warrants an investigation".
Meanwhile, Sinn Féin's Spokesperson on Health and Children Caoimhghín Ó Caoláin said that he was disappointed with the terms of reference.
He said that "there will be a number of people who will be bitterly disappointed by their exclusion from the inquiry into Mother and Baby Homes".
Today's announcement of Judge Murphy's terms of reference comes seven months after worldwide publicity surrounding historian Mary Corless' revelation that almost 800 children had died in Tuam's former mother-and-baby home in Co Galway between 1925 and 1961.
Witnesses had also reported seeing corpses in the institution's sewer.
Soon a multitude of babies' bodies was reported to be lying in unmarked graves in many of Ireland's seven remaining Catholic-run homes.
Ms Corless wants the commission to discover all such burial places and why the residents suffered from malnourishment.
Sally Mulready, a former resident of a Catholic mother-and-baby home who sits on the Council of State, said she would be appalled if the Government fails to pay redress to the small number of survivors of the Protestant Bethany Home.
In 2010, the Bethany Home Survivors' Group found over 200 unmarked graves of Protestant babies in Dublin.