With one exception, Aegon and his sisters destroyed or subdued any king who refused to recognize Targaryen overlordship. The Targaryens eventually gave up their foreign gods and accepted the faith of the Seven. Their dragons shrunk and eventually died out. The Targaryens kept the practice of polygamy and royal incest. Brothers married sisters, aunts married nephews, and uncles married nieces. This was a religious and cultural abomination to most Westerosi but the Targaryens rarely concerned themselves with the opinions of lesser people. However this non-forking family tree caught up with House Targaryen as more kings showed signs of instability. Three centuries after the Targaryens crowned themselves as rulers, their mental frailty reached its nadir under Aerys the Mad, a rapist and tyrant, who murdered Eddard Stark's father, brother and several other men when they challenged him to account for his son Rhaegar Targaryen, who had kidnapped Lyanna Stark. The realm erupted in revolt. The war ended with Jaime Lannister murdering the Mad King, Robert Baratheon killing Rhaegar Targaryen and taking the throne for himself, and the Lannisters murdering Targaryen women and children to forestall any future succession threats.
There is one Targaryen still left alive. She has dragons, though little else. Daenerys Targaryen believes herself to be the rightful ruler of all Westeros, though she has never seen it. She was conceived in the rebellion's final month and has been on the run ever since. Dragons are the nuclear weapons of Westeros warfare. Few people would dare to oppose anyone who controls full grown dragons. The Targaryen words are "Fire and Blood" which is exactly what they have traditionally given anyone unwise enough to challenge them. Time will tell if Daenerys has inherited her ancestors' cruelty and majesty or their unsteadiness (her parents were siblings after all)
When the Targaryens invaded, House Martell avoided open battle where the dragons could be successful but led a long guerrilla struggle that eventually forced the Targaryens to withdraw. The Targaryens invaded again and failed. Finally, the Targaryens smartened up and arranged marriages between themselves and the Martells. Dorne joined the realm peacefully. House Martell became a reliable supporter of the Targaryen dynasty.
Dornish people can range widely in skin tone. Martin has described Dornish as having skin shades similar to paler northerly folks or being "tanned","olive skinned" or "brown skinned". Dorne seemingly shares some features with Moorish Spain, Wales, North Africa, Italy or Palestine. It will be interesting to see how HBO, which has been willing to cast people of color, will cast Dornish actors. I think people like Ioan Gruffudd, Antonio Banderas, Maria Grazia Cucinotta, Thandie Newton, Jean Reno, Freida Pinto, Naveen Andrews, and Wentworth Miller could all conceivably be a Dornish type.
Elia Martell was the wife of Targaryen heir, Rhaegar Targaryen. During the sack of King's Landing it was Lannister bannermen, primarily The Mountain, who raped and murdered Elia Martell and her babies. House Martell has a well deserved reputation for neither forgiving nor forgetting. Elia Martell was the sister of Dorne's ruler, Prince Doran and his hotheaded younger brother Prince Oberyn. These past Lannister atrocities are why Cersei Lannister was opposed to Tyrion sending her daughter Myrcella to Dorne for betrothal and safekeeping. Dorne has ancient rivalries with The Stormlands (Baratheon) and The Reach (Tyrell). The regions have warred and raided for generations. Dorne is physically isolated behind mountain ranges and has more trade with the east than with the rest of Westeros.
The Martell sigil is a spear joined with the Sun. The Sun was the sigil of Nymeria and the Rhoynar while the spear was the sigil of the pre-Nymeria Martells. The Martell words are "Unbowed, Unbent, Unbroken" which refers to the fact they joined the kingdom because they wanted to, not because Targaryens made them. As far as House Martell is concerned, no one can make them do anything.
Like House Martell , House Arryn rules over an isolated portion of Westeros, The Vale. The Vale is a peninsula surrounded on three sides by water and on the fourth by mountains.
Before the events in A Game of Thrones House Arryn was ruled over by Jon Arryn, an older Lord who had fostered Ned Stark and Robert Baratheon as youngsters. When the Mad King killed Ned Stark's relatives and friends (including one of Jon Arryn's nephews), he ordered Jon Arryn to send him the heads of Ned Stark and Robert Baratheon. Arryn refused and called his banners. The realm erupted in revolt with Houses Stark, Tully, Arryn and Baratheon uniting to overthrow the mad king. Robert Baratheon became King and appointed Jon Arryn as the Hand.
The widowed Jon Arryn married Lysa Tully, Catelyn's younger sister. He was significantly older than she. After many miscarriages, Lysa bore Jon a son, (Robin in the HBO series, Robert in the books) who is roughly six years old at the story's beginning. Upon Jon's death (and presumed murder) his son becomes the Lord of The Vale.
Because of Robin's age, his mother Lysa wields all authority as regent. The boy is sickly, weak and uncomfortably close to Lysa, who has refused to wean him. She has also declined to let Robin be fostered anywhere, which is the usual practice for noble youth. With the war, one would have expected that House Arryn would come to the assistance of Houses Tully and Stark, but so far Lysa has refused to call the banners.
The Arryns rule from their mountainous Eyrie, a place that is virtually impregnable to attack. It's hard to get to the Eyrie but it's easy to leave. There is a "Moon Door" which opens to a six hundred foot drop to the mountainside. Lysa and especially Robin seem to have grown fond of "making bad men fly". There has generally been peace in The Vale, with the notable exception of the Mountain Clans, poorly armed groups that rob and kill travelers, but who generally avoid direct conflict with the better armed and organized Knights of the Vale. The Arryn words are "As High as Honor". These words hearken back to their legendary founding as well their mountains, chivalry and religious dedication.