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Thane (/ˈθeɪn/; Scottish Gaelic: taidhn) was the title given to a local royal official in medieval eastern Scotland, equivalent in rank to the son of an earl, who was at the head of an administrative and socio-economic unit known as a thanedom.
[T]he "thane", though he later developed into a laird, was at first an officer, half royal servant and half landowner, who looked after a portion of the king's land.— John Duncan Mackie, 
The earliest documentary record of a thane is in the written judgement of a land dispute settled at a provincial assembly of Fife between 1128 and 1136, at which one attendee is described as the thane of Falkland. A further eleven thanes are recorded over the course of the rest of the 12th century, attached to estates from East Lothian to Moray, all of which were at the time under the control of the King of Alba. From around the beginning of the 13th century a few thanes also start to be documented attached to estates under the control of earls, including Dunning and Strowan, which both lay within the Earldom of Strathearn. A statute of 1221 explicitly allowed that some thanes could be responsible to an earl rather than the king, though the overwhelming majority of thanes in the historical record were attached to lands that lay outside earldoms and were in royal hands.
The thane was introduced in the reign of David I (reigned 1124–1153), an Anglophile, to replace the Gaelic tòiseach (meaning leader, and with which the term Taoiseach shares an origin). In Scotland at that time toshach designated a deputy to a mormaer, controlling a particular portion of a mormaerdom on the mormaer's behalf. The English thegn was a more general term, simply referring to landholders of widely varying importance. Having introduced earl to describe mormaers, David used thane to describe toshachs.
Functionally, the thane was a territorial administrator, acting under a territorial earl (the latter resembling a Saxon ealdorman rather than the more superficial Norman earl), or royal steward. 12th century evidence makes it clear that the thane's key role was to collect revenue and services from the estates they administered, being permitted to keep some for themselves as "thane's right" (Latin: ius thani). Though thanes often held land within the region they administered, this was coincidental; providing land tenure was simply the way of paying for their services, the location of their lands not being intrinsically linked to the authority they wielded in any particular region.
However, after the death of Alexander III in 1286, thanes differed from their tosach forebears by holding their position as a feudal grant from the crown, rather than the almost independent status held by a tosach. Thanes consequently resembled English barons, but with greater judicial and administrative authority which extended beyond the lands they directly held. In later centuries, the term thanes dropped out of use in favour of baron, but described as having regality, a term used to describe both the thanes' powers, and the greater powers of the territorial earl.
In William Shakespeare's Macbeth (1606), the character Macbeth holds the title "Thane of Glamis", and later, "Thane of Cawdor". The historical King Macbeth fought a Thane of Cawdor who died in battle, but he did not thereby acquire the title himself.
The 2nd Earl of Cawdor wrote a history of the Thanes of Cawdor, in 1742, published in 1859.
In the video game The Elder Scrolls V: Skyrim, the player character is able to receive the honorary title of Thane of Whiterun (and other "holds") by completing quests for the local Jarl. The title allows the player to purchase land within various holds, such as Whiterun or Falkreath.
As we cannot name the first Celtic chieftain who consented to change his style of Toshach and his patriarchal sway for the title and stability of King's Thane of Cawdor, so it is impossible to fix the precise time when their ancient property and offices were acquired.