His/Her Imperial Highness (abbreviation HIH) is a style used by members of an imperial family to denote imperial - as opposed to royal - status to show that the holder in question is descended from an Emperor rather than a King (compare His/Her Royal Highness).
Today the style has mainly fallen from use with the exception of the Imperial Family of Japan (in Japanese: 殿下, denka). In the past, the style has been applied to more senior members of imperial dynasties, including the French, Russian imperial houses, among many others. Archdukes of Austria from the Habsburg dynasty held the style of Imperial and Royal Highness (in German: Kaiserliche und königliche Hoheit), with the "Royal" signifying their status as Princes of Hungary and Bohemia. They were also addressed as "Imperial Highness" (Kaiserliche Hoheit). The last Shah of Iran Mohammad Reza Pahlavi also used the style HIM, (His Imperial Majesty) and since the revolution the Imperial Pahlavi family still use the style HIM, such as for Farah Pahlavi. Members of the British royal family, theoretically, as the imperial family of India could have used the title, but did not.