They have beaten West Indies, England and Pakistan and now Ireland are targeting London on Thursday when they expect to be given Test match status by the International Cricket Council.
In February, the ICC agreed "in principle" that this week's meeting in London had "the potential to include additional Full Members (Ireland and Afghanistan subject to both meeting Membership criteria)”.
Cricket Ireland understand there have been no hiccups since and they stand ready to take their place alongside the game's established powers.
It is all a far cry from the years when the highlight of Ireland’s season was the visit for a one-off match by the touring Test team to England or, in alternate years, a two-day game at Lord’s against MCC, invariably made up of Minor County players.
The old Irish Cricket Union was founded in 1855 – Phoenix Cricket Club, founded 25 years earlier, is one of the oldest in the British Isles – but it was not until more than a century later that the Ireland team first made the rest of the cricket world take notice.
On July 2 1969, Ireland dismissed the West Indies for just 25 at Sion Mills in a match recorded for all time by television.
It has gone into folklore that the West Indies, who had flown in the night before, after the conclusion of the Lord’s Test, had immediately availed themselves of some typically generous Irish hospitality.
But whatever the truth of that, they were bundled out in 25.3 remarkable overs.
Ireland knocked off the runs for the loss of one wicket, but with the game over so quickly, the teams agreed to play on and West Indies even had a second innings, reaching a more respectable 4-78, after Ireland had declared on 8-125.
Ireland were admitted to England’s 60-over one-day competition, the Gillette Cup, in 1980 and almost made a dramatic impact, reducing Middlesex to 5-67 when the county replied to Ireland’s modest 102.
But it was to be another 17 years before Ireland claimed their first victory in the competition, in a home match against Middlesex, when the late South Africa captain Hansie Cronje was Ireland’s overseas professional.
By that stage, Ireland had been given Associate Membership of the ICC and after three failed attempts to qualify for the World Cup, they used home advantage in 2005 to reach the finals in the West Indies in 2007.
It took only two matches for them to make their mark on the world stage.
After tying with Zimbabwe in their opening fixture, they turned up on St Patrick's Day to see a green pitch at Sabina Park for their match against Pakistan, and a sea of green in the crowd as thousands of Ireland fans took over the ground.
Ireland bowled out the number-four ranked team for 132 and won by seven wickets in what was Bob Woolmer’s last match as Pakistan coach.
Tragically, the former England batsman was found dead in his hotel room the following morning.
When, three weeks later, Ireland beat Bangladesh in Barbados they joined the ODI rankings table and have been there ever since.
The celebrations back home in Ireland after the Pakistan win were nothing compared to those four years later when England were toppled in Bangalore, the day Kevin O’Brien became a world famous name with a 50-ball century – still the fastest ever in a World Cup – as Ireland chased down England’s 327.
The 2015 World Cup finals saw Ireland claim two more Full Member scalps as Phil Simmons inspired his adopted team against both his native West Indies and then Zimbabwe, each time with totals of more than 300.
Given all these achievements, it's little wonder Ireland feel ready to be put on a level playing field with the other 10 Full Members.