The Kingdom of the River and the Hills was one of the independent kingdoms of Westeros ruled by the First Men until the Andal Invasion. It was established on the modern Riverlands and took its name from the river Trident.
In the books
In the A Song of Ice and Fire novels, the Kingdom of the Rivers and the Hills was one of the many kingdoms established by the First Men. At some point it extended over much of the Riverlands, from the Trident to the Neck. It was ruled by House Mudd from their castle posthumously named Oldstones.
House Mudd was the last First Men dynasty to rule over the Trident. The kingdom later fell during the Coming of the Andals. It may not have ruled over the entire area of the modern Riverlands, given that every minor lord called himself a king during this era. The Mudd kingdom was centered around Oldstones on the Blue Fork of the Trident. For the next five thousand years the Riverlands continued to be a borderzone between strong Andal kingdoms which were established in Westeros. In the centuries leading up to the Targaryen Conquest, the Riverlands were conquered and ruled by the Storm Kings for three hundred years, until the Riverlands were taken from the Kingdom of the Stormlands by the Kingdom of the Iron Islands three generations before the Targaryen Conquest. The ironborn under House Hoare continued to dominate the Riverlands up until the time of the Targaryen Conquest, when the Riverlords led by Edmyn Tully revolted against their ironborn overlords in favor of Aegon the Conqueror.