Following the partition of Ireland, the Football Association of Ireland (FAI) was formed in Dublin in 1921. This was primarily as a response to alleged bias of the Irish Football Association (IFA) based in Belfast towards teams from Ulster.
The first international played by a team representing the FAI took place in the 1924 Paris Olympics as Bulgaria were defeated 1-0. The first match played in Dublin occurred in 1927 as Italy 'B' ran out 2-1 winners.
Skirmishing took place between the two bodies right up until 1950 when eventually FIFA's will was imposed and both ceased selecting players from the other's territory - the names Republic of Ireland and Northern Ireland first appeared around this time.
The FAI had only commenced the practice (in 1936) of selecting players from the whole of Ireland because the IFA would not stop selecting players from the whole of the island, yet had demanded that the FAI only select players from the south. Confused? Well, that was Irish football politics.