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Grand duke is the usual and established, though not literal, translation of these terms in English and Romance languages, which do not normally use separate words for a "prince" who reigns as a monarch (e.g. Albert II, Prince of Monaco) and a "prince" who does not reign, but belongs to a monarch's family (e.g. Prince William, Duke of Cambridge). German, Dutch, Slavic and Scandinavian languages do use separate words to express this concept, and in those languages grand prince is understood as a distinct title (for a cadet of a dynasty) from grand duke (hereditary ruler ranking below a king).
The title of grand prince was once used for the sovereign of a "grand principality". The last titular grand principalities vanished in 1917 and 1918, the territories being united into other monarchies or becoming republics. Already at that stage, the grand principalities of Lithuania, Transylvania and Finland had been for centuries under rulers of other, bigger monarchies, so that their title of grand prince was "masked" by a royal title (king/tsar) or an imperial one (emperor). The last sovereign to reign whose highest title was grand prince was Ivan IV of Moscow in the 16th century, until he assumed the style Tsar of Russia. When Ivan IV's pre-tsarist title is referred to in English, however, it is usually as grand duke.
Velikiy knjaz is also a Russian courtesy title for members of the family of the Russian tsar (from the 17th century), although those grand princes were not sovereigns.
Medieval use 
Grand Prince, used in the Slavic and Baltic languages, was the title of a mediæval monarch who headed a more-or-less loose confederation whose constituent parts were ruled by lesser princes. Those grand princes' title and position was at the time usually translated as king. In fact, the Slavic knjaz and the Baltic kunigaikštis (nowadays usually translated as prince) are cognates of king. However, a grand prince was usually only primus inter pares within a dynasty, primogeniture not governing the order of succession. All princes of the family were equally eligible to inherit a crown (for example, succession might be through agnatic seniority or rotation). Often other members of the dynasty ruled some constituent parts of the monarchy/country. An established use of the title was in the Kievan Rus' and in the Grand Duchy of Lithuania (from the 14th century). Thus, Veliki Knjaz has been more like high king than "grand duke", at least, originally and were not subordinated to any other authority as more western (for example Polish) Grand Dukes were. As these countries expanded territorially and moved towards primogeniture and centralization, their rulers acquired more elevated titles.
Великий князь (Velikiy Kniaz; literally, great prince) was, starting in the 10th century, the title of the leading Prince of the Kievan Rus', head of the Rurikid House: first the prince of Kiev, and then that of Vladimir and Galicia-Volhynia starting in the 13th century. Later, several princes of nationally important cities, which comprised vassal appanage principalities, held this title (Grand Prince of Moscow, Tver', Yaroslavl', Ryazan', Smolensk, etc.). From 1328 the Grand Prince of Moscow appeared as the titular head of all of Russia and slowly centralized power until Ivan IV was crowned tsar in 1547. Since then, the title grand prince ceased to be a hereditary office and became a generic title for members of the Imperial family until the Russian Revolution of 1917.
The Lithuanian title Didysis kunigaikštis was used by the rulers of Lithuania, and after 1569, it was one of two main titles used by the monarch of the Polish-Lithuanian Commonwealth. The kings of Poland from the Swedish House of Vasa also used this title for their non-Polish territories. This Lithuanian title was sometimes latinized as Magnus Dux or Grand Duke.
In 1582, king John III of Sweden added Grand Prince of Finland to the subsidiary titles of the Swedish kings, however without any territorial or civic implications, Finland already being a part of the Swedish realm.
After the Russian conquests, the title continued to be used by the Russian emperor in his role as ruler of Lithuania (1793–1918) and of autonomous Finland (1809–1917) as well. His titulary included, among other titles: "Grand Duke of Smolensk, Volynia, Podolia", "Lord and Grand Duke of Nizhni Novgorod, Chernigov" etc.
Modern use 
A more literal translation of the Russian title than grand duke would be great prince — especially in the pre-Petrine era — but the term is neither standard nor widely used in English. In German, however, a Russian Grand Duke was known as a Großfürst, and in Latin as Magnus Princeps.
Grand prince remained as a dynastic title for the senior members of the Romanov dynasty in Russia's imperial era. The title Velikiy Kniaz, its use finally formalized by Alexander III, then belonged to children and grandchildren (through sons) of the emperors of Russia. The daughters and paternal granddaughters of Russia's emperors used a different version of the title from females who obtained it as the consorts of Russian grand princes; the form for the latter was Великие Княгини, Velikie knjagini.
Styles and forms of address 
In modern times a Russian Grand Duke or Grand Duchess is styled Imperial Highness.