Postal addresses in Ireland are similar to those in the rest of the English-speaking world, but there is no national post code system. However, Dublin is divided into postal districts, under a system which was similar to that used in cities elsewhere in Europe until the introduction of postcode systems in the 1960s and '70s.
At the time, Ireland did not follow suit, and An Post did not introduce automated sorting machines for mail until the 1990s. By then, the introduction of new technology, known as Optical Character Recognition (OCR), meant that machines could 'read' whole addresses as opposed to just postcodes. Consequently, mail to addresses in the rest of the Republic does not require any digits after the address, eg:
ROI