They have never before reached the finals of the European Championship, but are just three points away from booking a spot in France next summer.
It has been 29 years since Ireland last played in a major international tournament, but following an impressive qualifying campaign they are on the verge of reaching Euro 2016.
Five wins from their opening seven qualifiers have lifted them to the top of Group F, where they sit one point above Romania and four ahead of Hungary.
It means that they only need three more points to book a first-ever appearance at the European Championship, after 13 unsuccessful qualifying campaigns.
Such an achievement seemed unlikely as they began their quest to reach the finals last September, as during their qualifying campaign for the 2014 World Cup, they recorded just one victory and finished a single point above Luxembourg in their group.
The pressure will be on Michael O'Neill and his players to perform in front of an expectant crowd in Belfast and they will want to make sure of reaching the finals with tricky games against Greece and Finland in their final two group matches.
Recent form: LLWDDW
Hoping to spoil Northern Ireland's party on Monday are a Hungary side who are firmly in with a strong chance of qualifying automatically for the Euros.
The result helped to solidify their position of third place in the group and they are currently five points clear of nearest challengers Finland, with a playoff place almost certain barring a late collapse.
They have been made to wait for an appearance at an international tournament, and just like Ireland, they too have not qualified for a major event since the 1986 World Cup.
It has been even longer since they last reached the European Championship, with the second and last of their appearances at the finals coming in 1972, where they finished in fourth place.
Recent form: WLDWWD
Northern Ireland will be hoping that Lafferty can continue his impressive goalscoring form when he leads the line on Monday evening.
The Norwich City striker has scored six goals in seven qualifiers, with only Robert Lewandowski scoring more during Poland's current campaign.
Lafferty and Chris Brunt would have missed the clash if they been cautioned against the Faroe Islands, but Jamie Ward is expected to remain on the sidelines with Niall McGinn keeping his place in the team.
Northern Ireland possible starting lineup:
McGovern; McLaughlin, McAuley, Evans, Baird; Davis, Brunt, Dallas, Norwood, McGinn; Lafferty
Hungary possible starting lineup:
Kiraly; Fiola, Juhasz, Kadar, Leandro; Stieber, Gera, Elek, Dzsudzsak, Szalai; Nikolic
Head To Head
Northern Ireland and Hungary met in the opening match of the qualifying campaign, with O'Neill's side claiming a 2-1 victory after late goals from McGinn and Lafferty.
It was Ireland's first away win in 18 matches and their first-ever victory over the Hungarians after four straight defeats.
Their last meeting in Belfast came seven years ago, when Sandor Torghelle and Gera scored in a 2-1 win for the visitors.
We say: Northern Ireland 2-1 Hungary
There is expected to be a fevered atmosphere inside Windsor Park on Monday, as Ireland stand on the verge of a remarkable achievement. The weight of a nation will be on the shoulders of their country's players, but they have risen to the challenge throughout this qualifying campaign. Hungary could prove difficult to break down, but we expect O'Neill's side to grind out a win that will secure a historic place at the European Championship.