It is typically used to address a prince or princess who is the child of the emperor and/or empress, or their spouse.
[1] The first dynasty to use the style in Europe on the generic basis were the Romanovs in the eighteenth century; the archdukes and archduchess of the House of Habsburg were only styled as Royal Highness given the officially elective nature of the Holy Roman Empire.
Following the Austro-Hungarian compromise with its creation of two intertwined but distinct states, the Austrian Empire and the Kingdom of Hungary, the style was changed to Imperial and Royal Highness to reflect the double role; however, the colloquialism of omitting "and Royal" was acceptable even for the most formal occasions.
Today, the style has mainly fallen from use with the exception of the Imperial House of Japan (Japanese: 殿下, Hepburn: denka).
Archdukes of Austria from the Habsburg dynasty traditionally hold the style of Imperial and Royal Highness (German: Kaiserliche und königliche Hoheit), with the "Royal" signifying their status as Princes of Hungary.