The Queen's historic visit to the Irish Republic has been described as a diplomatic success. Politicians from all sides said the trip signalled the beginning of a new era in Anglo-Irish relations.
David Cameron said the speech made by the Queen in Dublin Castle on Wednesday night had struck a chord with many people.
"What she said about things that could have been done differently or not been done at all, I think will have spoken volumes to people in Ireland," the Prime Minister said.
A Buckingham Palace spokeswoman said the Queen and Duke of Edinburgh have been delighted by the welcome they have received.
"The mood is very buoyant in the household. The visit will be in the Queen's mind for a very long time when she returns home," she said.
"Everybody in the household has been overwhelmed by the warmth of the welcome. It has been an extraordinary visit."
Sinn Fein also acknowledged the impact of the visit.
Deputy First Minister Martin McGuinness said the speeches made both by the Queen and President Mary McAleese were thought provoking.
The itinerary for the third day of the trip took what many considered to be a more relaxed tone - with a visit to the Irish countryside.
There was some sadness, however, after it emerged the country's popular former prime minister Garret FitzGerald had died at the age of 85.
The monarch met industry representatives and viewed a number of the horses at the Irish National Stud in County Kildare.
A keen horse-racing fan, she also watched as a jockey trained on a special horse simulator.The evening celebrations hosted by the British Embassy included performances by X Factor star Mary Byrne, Westlife and Riverdance.
There were also shows from fashion designers Victoria Beckham and John Rocha.
The first official royal visit since independence has taken place amid the biggest security operation ever mounted in the state, with thousands of police and armed soldiers on the streets of the capital.