Renly Baratheon pragmatically summed it up in A Clash of Kings (p. 265/761 of the 1999 Bantam paperback):
Tell me, what right did my brother Robert ever have to the Iron Throne? Oh, there was talk of blood ties between Baratheon and Targaryen, of weddings a hundred years past, of second sons and elder daughters. No one but the maesters care about any of it. Robert won the throne with his warhammer.
