James, the 5th High Steward, fought with the Robert the Bruce and secured the ongoing privileged position for the family.

Sir Walter Stewart married the Bruce's daughter Marjorie.  On the death of Bruce's only son David II, Sir Walter's son and Bruce's grandson, Robert Stewart became Robert II.

The Stewart Royal line continued with male heirs until Mary Queen of Scots.  The Stuarts held the Scottish throne with Robert II from 1371 (later the English and British) until Queen Anne in 1714.  But of course, after the Hanoverian line was placed on the throne, the Royal Stuart line continued through uncrowned James VIII and James Francis Edward Stuart, Bonnie Prince Charlie.  Jacobite rebellions continued up until the final defeat at Culloden in 1746.

The family had many branches including Stewart & Stuarts in Perthshire.

Garth Castle near Aberfeldy was built in 14thC by the 'Wolf of Badenoch', Alexander Stewart, Earl of Buchan.

During the reign of Robert III his brother Robert Stewart, Duke of Albany, acted as Regent.  (Robert III was actually John but took the name Robert because John was felt to be too 'English').  Doune Castle is an impressive fortress built late in the late 14thC by Robert, Duke of Albany. Robert, Duke of Albany continued initially as Regent for James I.  This Regency was in turn continued by his son Murdoch, Duke of Albany. James I had his Murdoch executed for treason and forfeited much of the Stewart lands including Doune Castle in 1424.

The Stewarts of Ardvorlich House on the south side of Loch Earn represent another smaller branch of the family.

James II gave the Earldom of Atholl centred on Blair Castle to a Stewart of Balvenie in 1457.  These Stewart lands passed to John Murray of Tullibardine through Stewart female decent in 1629.

Source: http://www.perthshire-scotland.co.uk/clans-stewart.htm