House Tyrell rules the south central area of Westeros known as The Reach. The Tyrells maintain order from their capital at Highgarden. The Reach is the most populated, most fertile and perhaps the most beautiful area of Westeros. The Tyrells can usually raise larger armies than anyone else. They also have a strong navy which can be compared to that of the royals and the Iron Isles. The Tyrells are also richer than any other group except the Lannisters. This potent combination of money and muscle makes the Tyrells either a useful ally or a bad enemy to have.
House Tyrell was originally a steward house to The Reach's rulers. When the ruling king perished in dragon fire fighting the Targaryen invaders, House Tyrell decided that further battle would be pointless and promptly surrendered to the Targaryens. For this self-interested practicality (flip-flopping??) House Tyrell was raised to ruling status over The Reach. The fact that House Tyrell was allied to the Targaryens almost certainly delayed the incorporation of Dorne into the realm as the Tyrells and the Martells were bitter and occasionally bloody rivals.
During Robert's Rebellion the Tyrells supported the Targaryens, and supplied many of their troops. Afterwards Robert forgave them. It is unwise to alienate the Tyrells not just because of their numbers but also because The Reach supplies (or can blockade) a goodly amount of the food consumed in King's Landing. The Reach is the continent's bread basket. The Reach is where rules about knighthood and chivalry are taken most seriously. The people of The Reach consider themselves to be quite cultured and civilized compared to other places.
|Grandma and Granddaughter|
Loras Tyrell asked Lord Eddard Stark for permission to lead the expedition to capture or kill the Mountain, a Lannister bannerman. Stark thought Loras was too young and inexperienced to lead. Stark denied that request and sent his own people, thereby missing an opportunity to drive a political wedge between the Lannisters and Tyrells and just as importantly, keep his own soldiers close. This proved to be a tragic mistake. Upon Robert's and Ned's deaths the Tyrells supported Renly Baratheon as king. They wed Margaery Tyrell to Renly Baratheon despite Renly's lack of any reasonably legitimate claim to the Iron Throne and his romantic preference for Margaery's brother Loras. After Renly's death, the Tyrells quickly and virtually seamlessly switched support to the Lannisters, betrothing the supposedly still virginal Margaery to Joffrey. The Tyrells like to be on the winning team. The Tyrell symbol is a yellow rose on a green field. Their words are "Growing Strong". This serves as a boast to their enemies. Their words also may remind their allies to keep a watchful eye on them. Margaery wants to be the Queen. Mace Tyrell wants to be the King's grandfather. Neither one of them may be too particular about who helps them achieve those goals.
Technically speaking King Joffrey is a member of this House as he does not believe the stories of his parentage. But as we and House Lord Stannis Baratheon both know, Joffrey is all Lannister so he doesn't belong here. House Baratheon was originally a bastard branch from House Targaryen. The House founder Orys Baratheon was Aegon the Conquerer's half-brother and Hand. The House intermarried with and supported the Targaryens over the generations. Robert Baratheon could boast relatively recent direct descent from a Targaryen lady, which is what he based his claim to rule when he took the throne. Well he based it on that and the fact that he caved in Rhaegar Targaryen's chest with his trusty warhammer.
House Baratheon controls the Stormlands, a central east portion of Westeros. The Stormlands are so called because of the extremely bad weather that pummels the coast and occasionally comes farther inland. House Baratheon has traditionally ruled from its capital of Storm's End. The Stormlands warriors and lords tend to be an independent group of hard cases. A strong hand is often needed to control them. When Robert called his banners to support his revolt, many supported the Targaryens instead. Robert had to defeat three separate loyalist armies among his own people. Similarly it was a source of massive frustration to Stannis that when he claimed House leadership and the Iron Throne after Robert's death, many of the Baratheon bannermen, disliking the dour, pedantic and legalistic Stannis, flocked to the charismatic and exciting Renly Baratheon. Brienne of Tarth is from the Stormlands.
In Season Two, Stannis Baratheon had Renly Baratheon murdered via magic (literally) conceived by his religious and sorcerous advisor Melisandre. Many Baratheon bannermen then chose to support Stannis but after his defeat at Kings' Landing it remains to be seen if Stannis will keep their loyalty. Stannis firmly believes himself to be rightful king of all Westeros. He doesn't care if he has one man following him or one hundred thousand. Stannis is skilled at holding grudges. After Robert became king he gave Stannis the island of Dragonstone to rule instead of the much richer (and more militarily valuable) Storm's End. Dragonstone was out of the way and had fewer sworn bannermen. As Robert was now king, Stannis thought that the Baratheon capital of Storm's End should be ruled by the Baratheon heir and next older brother, that is to say Stannis. Stannis felt insulted and took this very personally, especially since he had provided critical service to his big brother during the war, including leading fierce resistance at Storm's End to an almost year long siege by Mace Tyrell. Stannis may have been reduced to eating shoe leather, among other less savory things, but he didn't give up. In a world of hard men, Stannis prides himself on being among the hardest. He doesn't boast. He just goes to work. Nevertheless he resents not getting what he sees as his due. As the quintessential middle brother he's resented things since childhood.
Robert probably didn't like Stannis very much but Dragonstone also had some former Targaryen supporters who needed a firm leader like Stannis to watch over them. On the other hand, if Renly hadn't been at Storm's End he may not have had support to challenge Stannis and would have had to be content with being named Stannis' heir. Stannis has no sons. House Baratheon has traditional rivalries with House Tyrell and House Martell. The House words are "Ours is the Fury" . This boast conflates the region's constant deadly storms with House Baratheon's martial spirit.