Numerous islands dot the northern coast of Sothoryos. These have been mapped, and the main island chain is known as the Basilisk Isles. West of the Basilisk Isles is the large island of Naath, whose musically-inclined inhabitants are famed for their devotion to pacifism. These islands are frequently raided by slavers.
The Summer Islands are known to lie off the northwestern coast of Sothoryos, far west of Naath.
When an assassination attempt is made on Daenerys Targaryen in Vaes Dothrak, she says she thought King Robert Baratheon would leave her alone after her brother Viserys Targaryen died. Ser Jorah Mormont then explains to her that as the last Targaryen, King Robert's agents will never stop hunting her no matter how far she flees, even if she goes to Asshai or the Basilisk Isles.
The far northern coast of Sothoryos appears in the title sequence once it changes to start including Qarth. Xaro Xhoan Daxos says he is originally from the Summer Islands, but rose to become a wealthy merchant leader in Qarth.
In the books
In the A Song of Ice and Fire novels, the northern coast of Sothoryos lies a few hundred miles south of Slaver's Bay and Valyria. This coastline and its cities was devastated in the Doom of Valyria four hundred years ago, which triggered tsunamis and tidal waves that inundated the coastlands. The ruins of the once-great cities of Zamettar and Yeen can still be seen near the coast.
Sothoryos appears to consist of deserts and jungles, and is home to certain species of hairy ape. Little else about it is known.
Sothoryos is loosely analogous to Africa, as Essos is to Eurasia. According to George R.R. Martin, Sothoryos is unexplored and largely unknown to the peoples living in the Seven Kingdoms and the Free Cities. What few parts they have visited on the northern coast are filled with plague-ridden jungles. The people of Sothoryos tend to be dark-skinned and many, such as the vegetarian and musically inclined inhabitants of Naath, are quite peaceful (the Naathi are vegetarians because they refuse to harm any living thing, even animals). Unfortunately this has made them prime targets for the slaving operations of the cities in nearby Slaver's Bay. As a result, it is not unusual to see dark-skinned peoples in Essos, either as slaves in Slaver's Bay, or those who won their freedom and went on to become merchants, pirates, mercenaries, etc.
On the title sequence map the north coast of Sothoryos is apparently wholly located in the Summer Sea. However, when George R.R. Martin altered his maps for The Lands of Ice and Fire (a companion map collection for the novels, not the TV series) he adjusted this so Sothoryos is now located at the southwestern end of the Jade Sea. The large island of Great Moraq lies in the western opening of the Jade Sea, between Essos and Sothoryos. The north coast of Great Moraq is divided from Essos by the Straits of Qarth, while the south coast of Great Moraq is divided from Sothoryos by the Cinnamon Straits.
The names "Sothoryos" and "Sothoros" have been used somewhat inconsistently in the books. A problem is that the continent as a whole is rarely referred to by name, because almost none of the narrative takes place there. Characters from regions of the continent most often simply refer to specifically what region they are from. In the fourth novel, for example, the name "Sothoryos" is only used in-text four or five times. The few text references have alternated between "Sothoryos" and "Sothoros" (leaving out the "y"). Meanwhile, all maps have consistently used the spelling "Sothoryos" (in A Feast for Crows, A Dance with Dragons, and The Lands of Ice and Fire), though past maps have been known to include spelling errors. Moreover, on two separate occasions George R.R. Martin has answered Q&A about the continent (in 2002 and 2012), and in these cases Martin himself used the spelling "Sothoryos".
Elio Garcia (aka "Ran"), the founder of Westeros.org and co-author of The Worlds of Ice and Fire book with George R.R. Martin, weighed in on the issue: "Sothoryos" is indeed the correct spelling, and as of 2012 this is the spelling that Martin uses in all of his correspondence and maps. "Sothoros" only appeared a few times because either Martin wavered on the spelling earlier in the series, or it was an error in the editing process, but Martin has officially settled on "Sothoryos" as the proper spelling.