Daenerys Targaryen's war for Westeros

Daenerys Targaryen's invasion of Westeros is a conflict that grew out of the end of the War of the Five Kings, when Daenerys Targaryen returned to Westeros with three live dragons, along with a large army of Dothraki and Unsullied, to reclaim the Iron Throne that her own father Aerys II Targaryen had been deposed from with his death at the end of Robert's Rebellion two decades before.

Prelude
Queen Cersei Lannister's grasp on the Seven Kingdoms fell apart until she killed many of her enemies in one fell swoop by destroying the Great Sept of Baelor with wildfire, in the process destroying the vital alliance with House Tyrell which was one of the few things backing up her exhausted armies and bankrupt crown.

Meanwhile, Dorne had already turned against the Lannisters and closed its borders at the Red Mountains to the south - combined with the Reach turning against the Lannisters, southern Westeros had fallen from their control.

Meanwhile, House Stark managed to retake the North from House Bolton - the Lannisters' puppets - with the help of House Arryn's large unblooded army, at which point The Vale of Arryn also openly declared against the Lannisters.

This left Queen Cersei with only control over King's Landing and The Crownlands, as well as the Lannisters' home territory in The Westerlands - and the weakly held, devastated Riverlands between the two, nominally until control of the Lannister-puppet House Frey but whose rule was ineffective at best and already crumbling.

The Iron Islands, meanwhile, remained split: Euron Greyjoy himself won the Kingsmoot election and was named king, but when she lost his niece Yara Greyjoy fled the isles with the core of the Iron Fleet and sailed to Meereen to ally with Daenerys herself.

After gaining armies and followers in Slaver's Bay, and then winning the loyalty of the Dothraki, Daenerys finally decided she was in a strong enough position to return to Westeros. Apart from her new alliance with Yara Greyjoy, Dorne and the Reach switched their support to Daenerys, and she also had the skilled counsel of her new Hand of the Queen - Tyrion Lannister, Cersei's own exiled younger brother seeking revenge.

In the books
In the A Song of Ice and Fire novels, Daenerys hasn't attempted to return to Westeros as of the fifth of most recent novel (corresponding to the end of Season 5 of the TV series for her storyline).

It is strongly implied that she will win over the Dothraki at some point as she did in Season 6.

Doran Martell is still alive in the TV series (his murder by Ellaria Sand in the TV series was a drastic condensation, rather, invention, of the TV series with no basis in the novels). Doran explains to his daughter Arianne that he intends to ally with Daenerys - thus she doesn't even need to conquer a beachhead, as the instant she arrives in Westeros Dorne will revolt against the Lannisters and join her other armies. Doran even sends his elder son Quentyn as an envoy to try to broker a formal alliance (though he is later killed surreptitiously trying to claim one of her dragons).

Yara Greyjoy doesn't go to Meereen in the novels: instead she fleets the Kingsmoot back to her captured holdings in the North - but her army camp is soon attacked by Stannis Baratheon, who takes her prisoner. Instead, it is her uncle Victarion Greyjoy (cut from the TV series) who takes the Iron Fleet] east to Meereen - but he plans to betray Euron by allying with Daenerys himself. In the TV version Yara takes Victarion's role, and instead of secretly planning to turn against Euron, openly does so.

The books make explicitly clear that the Iron Fleet isn't the only fleet in the Iron Islands, just their "national fleet" of sorts - the best ships and crews, under direct command of their king. Each of the local Houses and isles have their own fleets. Thus in both versions, even though Victarion/Yara took their "best ships", Euron would still have a considerable fleet left at his command (even without needing to build new ones to replace his losses).

The Lannisters, meanwhile, are already half-exhausted and bankrupt. Robb Stark's campaign did succeed in slaughtered around half of their armies and they cannot simply replace them for years to come. The Iron Throne is in astronomical debt and the Iron Bank of Braavos has lost faith in them. The TV version claimed this is because their gold mines ran dry - which is a gross exaggeration and physically impossible. In the books, spending simply outpaced the rate of production (just because they have gold mines doesn't mean they produce infinite amounts of gold).

Littlefinger's plans have also been drastically altered in the TV series. In the books, his plan is to have Sansa Stark marry Harrold Hardyng, Sweetrobin Arryn's cousin and closest living relative. He then intends to poison Robin, and have Sansa urge the Vale lords to remember their vows to her father Ned Stark and use their massive, unbloodied army (of around 20-30,000 men) to retake the North from the Boltons (who, at best, only have around 6,000 men, and are already fighting both Stannis and the other Northern Houses). It is unclear how Daenerys factors into Littlefinger's plans, or if he has even considered her arrival yet (though his cryptic references to "three queens" in Westeros after the "War of the Five Kings" imply he is somewhat aware of her).

This page is not titled the "Targaryen Restoration" - because that assumes that Daenerys will succeed (it is entirely possible she may be killed by the White Walkers or other means before that).