It will look at claims of abuse - some against high-profile figures - and its alleged cover-up by councils, the courts, schools, the church, the BBC and the Army, by assessing whether these institutions failed in their duty of care to protect children.
On Thursday, the inquiry finally opens, chaired by Justice Lowell Goddard, a judge from New Zealand. But the inquiry has been an almost constant headache for Mrs May.
Two proposed chairs - Baroness Butler-Sloss and Fiona Woolf - stood down amid criticism that there were too close to the Establishment, and the process has been beset by delays and wrangling over the terms of reference.
Opening the inquiry in London on Thursday, Justice Goddard said: "We want to hear from any individuals who were sexually abused as children in an institutional setting such as a care home, school or religious institution, anyone who reported abuse to a person in authority such as a police officer, social worker or teacher where the abuse was ignored or not properly acted upon."
Here's what you need to know about the inquiry.
What are the allegations?
The inquiry was set up last year after it emerged that a dossier of child sex abuse allegations was sent to the late Leon Brittan, during the time he was home secretary in the 1980s.
The dossier, prepared by Geoffrey Dickens, was said by the late Tory MP's son to have contained "explosive" allegations against powerful and famous people, including politicians. But it has been lost by the Home Office.
Among others, former Labour MP Lord Greville Janner, currently being prosecuted for the alleged indecent assault of minors, could be called to give evidence.
The range of institutions being looked at by the inquiry is broad; a huge amount of evidence will be heard.
Justice Goddard said on Thursday that she would look at allegations against prominent people and politicians, and at institutions including faith organisations, the criminal justice system, councils, the NHS, the BBC and the Ministry of Defence.
The inquiry covers England and Wales, and notices have been sent to 243 institutions to hold on to child care records.
How many victims and survivors are there?
Hundreds. More are coming forward all the time. There are believed to be more than 600 current police probes sexual abuse, 261 of which are described as "non-recent", in the jargon.
Will anyone be prosecuted as a result of the inquiry?
Justice Goddard has said the inquiry will name individuals and organisations, and pass allegations to police.
Who is on the panel?
The members of the five-strong panel are: Justice Lowell Goddard, its chair; Prof Alexis Jay of Strathclyde University; Drusilla Sharpling of the police inspectorate; Prof Malcolm Evans, Bristol University; Ivor Frank, a barrister specialising in child protection.
Child abuse survivors will sit on the inquiry's Victims and Survivors Panel.
How long will it last?
There is no cut-off point in the inquiry's terms of reference - but Justice Goddard said that she hopes that it will be done by 2020.
But others Keith Vaz MP, chair of the Home Affairs Select Committee, said it could last a decade." Go to: http://www.independent.co.uk/news/uk/politics/child-sex-abuse-inquiry-6-things-you-need-to-know-10377571.html