They held estates in England, granted during the reign of King William Rufus.
One member of the family, John Balliol, was named King of Scotland after the disputed succession following extinction of the Dunkeld line.
John was deposed, leading to the First War of Scottish Independence.
The last two on the list both had English support for their claims but both were deposed.
Edward died without issue, but the Balliol descent continued through his cousin Christine de Lindsay (granddaughter of John I), who married Enguerrand V, Lord of Coucy, to the lords of Coucy and ultimately the Bourbon kings of France and Spain.