There is an excellent description of clan tartans over at wikipedia, which I will reprint a portion of below:
It is generally regarded that "clan tartans" date no earlier than the beginning of the 19th century. It is maintained by many that clan tartans were not in use at the time of the Battle of Culloden in 1746. The method of identifying friend from foe was not through tartans but by the colour of ribbon worn upon the bonnet. David Morier's well-known painting of the Highland charge at the Battle of Culloden shows the clansman wearing various tartans. The setts painted all differ from one another and very few of the those painted show any resemblance to today's clan tartans. Contemporary portraits show that although tartan is of an early date, the pattern worn depended not on the wearer's clan, but upon his or her location, or personal taste. The idea of groups of men wearing the same tartan is thought to originate from the military units in the 18th century. Evidence suggests that in 1725 the Independent Highland Companies may have worn a uniform tartan.
The naming and registration of official clan tartans began on April 8, 1815, when the Highland Society of London (founded 1778) resolved that all the clan chiefs each "be respectfully solicited to furnish the Society with as Much of the Tartan of his Lordship's Clan as will serve to Show the Pattern and to Authenticate the Same by Attaching Thereunto a Card bearing the Impression of his Lordship's Arms." Many had no idea of what their tartan might be, but were keen to comply and to provide authentic signed and sealed samples.
Today tartan and "clan tartan" is an important part of a Scottish clan. Almost all Scottish clans have several tartans attributed to their name. Several clans have "official" tartans. Although it is possible for anyone to create a tartan and name it any name they wish, the only person with the authority to make a clan's tartan "official" is the chief. In some cases, following such recognition from the clan chief, the clan tartan is recorded and registered by the Lord Lyon King of Arms. Once approved by the Lord Lyon, after recommendation by the Advisory Committee on Tartan, the clan tartan is then recorded in the Lyon Court Books. In at least one instance a clan tartan appears in the heraldry of a clan chief and is considered by the Lord Lyon as the "proper" tartan of the clan.
Cumming - Ancient (wr1158)
Cumming - Modern (wr1157)
Cumming - Hunting (wr1991)
Comyn Cumming Buchan (wr2012)
Cumming Wilsons of Bannockburn (wr508)
Cumming of Glenochy (wr1902)