Ireland's President Michael Higgins today praised the "warm friendship" with the UK as he became the first Irish head of state to address the House of Parliament.
Mr Higgins said the links between the two countries were now "strong and resolute" and there was now "mutual respect" despite historical differences.
The Queen and the Irish President Micheal D Higgens have been viewing Irish items in the Royal collection in Windsor as part of the historic state visit.
President Higgins will address the Houses of Parliament later this afternoon, before the royal banquet this evening.
Irish President Michael Higgins has made history today by becoming the first ever Irish President head of state to visit the UK.
He was greeted by the Queen and Duke of Edinburgh at Windsor Castle today along with his wife Sabrina Higgins.
The Queen and the President of Ireland stood side by side to observe the Irish Anthem being played by a military band in Windsor, during the first visit to the UK by an Irish head of state.
The anthem was played after the President Higgins and Michael Higgins were honoured with two separate gun salutes, and Mr Higgins and Philip inspected troops of the Queen's Company, Genadier Guards.
Major Andrew Seddon, captain of the Queen's Company Grenadier Guards, invited Mr Higgins to inspect the guard of honour, speaking to him in Irish. The Irish Guards was represented by their regimental band as the troops are currently on peacekeeping duties in Cyprus.
President Higgins presented a new ceremonial red coat to its regimental mascot, an Irish wolfhound called Domhnall of Shantamon.
The Irish flag is hanging outside Windsor Castle as the Queen prepares to welcome the Irish President for the first state visit in history.
Crowds have started to gather along the route, ahead of Micheal D Higgins' momentous meeting with the Queen.
Although President Higgins has travelled to events in London, Manchester, Liverpool and Scotland last year, these were not official visits.
Today's ceremonial visit will begin at the Irish Embassy, when the Prince of Wales and The Duchess of Cornwall will greet The President and Mrs Higgins, on behalf on the Queen.
They will then journey together to Windsor.
Irish President Michael D Higgins said today's historic state visit to the UK was not about "forgetting the past" or "wiping the slate clean" but about focusing on the present and building future relations. It is the first official state visit from Ireland to its former colonial ruler.
Speaking to Irish state broadcaster RTE he said progress should not be about forgetting the past.
"The challenge is to hand to a future generation all of the prospects of the future. You are not inviting them to an amnesia about any deep dispute.
"There are a lot of very difficult memories and it would be to my mind wrong to suggest to anyone that you should as it were, wipe the slate clean."
The President will be joined on the trip by Irish Taoiseach Enda Kenny and Foreign Affairs Minister Eamon Gilmore.
It's an historic day for the Queen and the Duke of Edinburgh today in Windsor.
They are due to meet the Irish President Michael Higgins.
There will be a traditional carriage procession through the streets to reach the castle.