Some are allowed to reopen but this is subject to guidelines being observed.
Under the Fáilte Ireland guidelines published in mid-June, only pubs which are also serving "substantial meals" costing €9 or more are allowed to open and serve alcohol.
Punters are required to book in advance, provide a contact for their group in case there is a need to follow up, and are only allowed to stay in the pub for a maximum of 105 minutes.
Physical distancing of "at least 2 metres" is required, unless specific requirements are met, in which case this drops to one metre.
In Dublin, over the weekend, huge crowds were pictured drinking on the streets outside bars and restaurants, with no evidence of physical distancing or wearing masks.
The problem has largely stemmed from the sale of takeaway pints, but there were also reports of people buying alcohol in off licences are drinking it on the street too.
Currently, alcohol can be sold for takeaway through a hatch from a licensed premises but it cannot be consumed within 100 metres of the premises where it was sold. Gardaí have the power to confiscate alcohol being consumed in a public place.
The Licensed Vintners Association (LVA), which represents Dublin pubs, has claimed it was "a small minority" of businesses which were selling takeaway pints which caused the problems but it hit out at those members which, it says, are "knowingly allowing that alcohol to be consumed on public streets and laneways" and said gardaí need to intervene.
The Restaurants Association of Ireland also described the scenes as "shocking" and said gardaí need enhanced powers to stop it happening again.
Over the weekend, some 6,000 checks were carried out by gardaí at pubs and restaurants all over the country, according to Garda Commissioner Drew Harris. Mr Harris noted some of these were repeat visits to the same premises, rather than 6,000 different pubs or restaurants.
This was part of Operation Navigation, which was prompted by "some licensed premises and their customers ignoring public health guidelines", and involved a wide, targeted check of licensed premises, rather than previous plans for spot checks.
Mr Harris said it may take some time to know how many - if any - of these checks translate into prosecutions for pubs, but said it was "not surprising" that some were flouting the rules.
He said the Dublin incident was dealt with as a public order situation.
Pub owners have been told that if they are found to be in breach of rules, it will count against them when it comes to renewing their licences later this year.
From July 20, other pubs will be allowed to reopen.
Currently, no additional guidelines have been published for these restaurants: the most recent information from Fáilte Ireland still refers to pubs serving food. This is a point raised by Cork publican Michael O'Donovan, who says many pubs are completely in the dark: some 60% of pubs outside of Dublin do not serve food and have not yet reopened.
With just two weeks to go before they should be allowed to reopen, they don't know what changes - if any - they will be required to make.
Currently, the roadmap identifies July 20 as the date of reopening - but that is a changeable document and Taoiseach Micheál Martin and Justice Minister Helen McEntee have both said the situation will be kept under review. Mr Martin said the July 20 date may be postponed if the number of Covid-19 cases starts to rise in the wake of the scenes in Dublin in recent days.