Clan Muir is a Scottish clan that is armigerous. Per certain sources, holders of the surname Muir (also appearing as Mure and Moore), of Ayrshire, have been noted as a possible sept of Clan Boyd, though this is not clearly identified to a reliable resource. A spelling variation More/Moore is a sept of Clan Leslie in Aberdeenshire, and, having genetic proof of Muirs in Aberdeenshire, may have roots in the Mure/Muir line of southwest Scotland.

However, there are other instances in which links to the Mure/Muir line of southwest Scotland cannot be confirmed. The surname Moir, for example, is a sept of Clan Gordon in the highlands, but is not part of this same group of Mure/Muir/Moore. A single family, the Mores/Moores of Drumcork, are septs of Clan Grant, but there is no evidence of a connection to the Mure/Muir line. Some also project Muir may be a sept of Clan Campbell, though even Clan Campbell considers this unlikely.

The Scottish surname Muir supposedly originated as denoting someone who lived beside a moor. The name is derived from the Scots form of the Middle English more, meaning "moor" or "fen".^{[citation needed]}

The first Mor/de Mor/de la Mor/Mure/Muir with solid documentation to Ayr, Scotland, is David de More. "The most ancient of the name on record are the Mores of Polkelly, near Kilmarnock; one of whom, David de More, appears as witness to a charter of Alexander II", between 1214 and 1249.

After David, the next most distant person found is Sir Gilchrist Mure/Muir (ca. 1200 - ca. 1280), in association with his part in the Battle of Largs, on 2 October 1263. Given the naming tradition, and locality (Ayr), it appears at least three descendants of his (Adam, Gilchrist, and Reginald/Ronald, all listed as "counte de Are/Ayr") appear in the Ragman Rolls, thirty-three years later. There were also three others with the surname listed, namely, Reynaud More de Cragg, del counte de Lanark, Symon de la More, de Thaugarfton, del counte de Lanark, and Douenal le fiz Michel More de Leuenghes, del counte de Dunbreton.

In 1291, a Thomas de la More was listed as executor of the Will of Dervorguilla de Balliol, mother of John Balliol, King of Scots.

Further, an Adam de la More, along with William de la More, were recorded as jurors on the lands of Lady Elena la Zuche, in Coyningham (Cunningham), in 1295. It seems likely that Adam was also one-in-the-same as holding lands in Ralston, Renfrewshire, in 1315 and 1321, and as the knight-possibly the same as the Adam who witnessed the charters of Robert the Bruce, King of Scots, between 1328 and 1329.

Polkelly seems to have been the "ancient" property held in Scotland by the Mures.^{[citation needed]}