The Tyrells were stewards to House Gardener, the Kings of the Reach, before the Targaryen conquest; after the Gardener line was extinguished in that war, Aegon the Conqueror made the Tyrells overlords in the Reach and Wardens of the South.
The Tyrells were stewards to House Gardener, the Kings of the Reach who on accasion married into the lesser house. After Targaryen extinguished house Gardener in that war of the Conquest, Aegon the Conqueror made the Tyrells lords paramount in the Reach, Lord of Highgarden and Wardens of the South.