Royal visit: Your views
The Queen is the first British monarch to make a state visit to Ireland since it became a republic.
During her four-day visit she laid a wreath at the Garden of Remembrance and visited Croke Park.
BBC News website readers from Ireland have been sharing their views:
Derek Hanlon, Dublin
I was in O'Connell street on Monday about half an hour before the Queen passed through and I decided to hang around to try and get a glimpse of her.
There was a very tense atmosphere in the place with protests taking place just up the road.
I don't think people knew what to do when she passed - we couldn't work out whether to clap or not but then everyone started applauding and cheering.
At that moment the tension disappeared. I got a glimpse of her and when she waved we waved back - it was a special moment.
I think it's great that she's visited Ireland. I read a lot of the negative comments by Sinn Fein but that's all in the past. It's time to move on now.
I don't think the Queen needs to apologise for anything, the only statement I hope she makes is that she's enjoyed her time here.
Sebastian Clare, Dublin
I've lived in Dublin for 22 years.
I think the majority of people here are either not bothered or positive about the visit.
However, because of the disruption on the streets caused by the visit, support might have dwindled a little - our capital has been almost empty because of the procession of state cars.
Although I have no opposition to state visits by elected heads, I object to the monarchy as a whole and feel uncomfortable at the idea of the bowing and scraping that takes place around a Royal visit.
One of the driving narratives of this visit is that we're putting our history to bed.
But we as a country had a revolution against the monarchy as head of state - so this makes the whole thing seem a little ironic.
I'm not particularly bothered by any place the Queen is visiting per se. However, I would have liked some sort of recognition of the anniversary of the Dublin Monaghan bombings, which was on Tuesday 17 May - even if it was only a vague mention.
Gavin Doyle, Dublin
Most people I know in Dublin are in favour of the state visit.
Some simply regard it as a good thing financially, to promote the country. Most however have a sense of the history and feel that this visit is long overdue.
It is a shame that the people were kept away from the streets where Queen Elizabeth II and the Duke of Edinburgh travelled.
As can be seen by the few members of the public who got near enough to cheer them at Trinity College, onlookers and well-wishers would outnumber people protesting on Parnell Street by 100 to one.
The media always tends to concentrate on the "dissidents" causing trouble in the streets, but these people are just ne'er-do-wells. My worry about this visit is that it might send an image to the world of the Queen not being welcome, but that is not the case.
I was in town yesterday in the city centre - it felt quite strange because there were police everywhere but it was quieter than usual.
I think it is very symbolic that the Queen visited the Garden of Remembrance.
The good thing that will come out of this visit is that Britain will become more aware of its nearest neighbour.
I welcome the Queen's visit and I hope this will be the beginning of the end of all the wrongs between Ireland and Britain.
However, I do think this is historically highly sensitive - particularly given some of the areas the Queen is visiting.
I am also saddened by the distinct lack of apology from the Queen for the Easter Rising in 1916 and for the 14 who were killed in Croke Park - especially as she has visited both of these places.
I still feel positive about her tour of Ireland, but I think some sort of acknowledgement would have topped it all off.
Generally the atmosphere in Dublin is quite positive. There hasn't been the spectator turnout that people were expecting but that's mainly because of the police presence and security.
On Monday the atmosphere in Dublin was quite tense - I think many people were expecting something bad to happen. Police were carrying out searches in O'Connell street.
On Tuesday the atmosphere was much lighter as people began to relax. The feeling - partly because of the football final - was very celebratory.