In Twilight Princess, the desert is only accessible with the help of a special function of Fyer's cannon at Lake Hylia, or by the Twilight Portal that Link opens up at Gerudo Mesa. The desert is filled with Peahats and Moldorms. Despite its name, no Gerudo are shown to reside here (or anywhere in the game, aside Ganondorf).
The Arbiter's Grounds is located in Gerudo Desert, which is the fourth dungeon and home to the Mirror of Twilight. Also, the Cave of Ordeals, a long mini-dungeon that has many floors full of enemies, home of the Great Fairy, is situated within Gerudo Mesa, where the large piece of the Bridge of Eldin that was teleported by Shadow Beasts was sent. Link can teleport the bridge part back to its original location in Eldin Province, not only repairing the Bridge of Eldin, but also opening the entrance to the Cave of Ordeals.
According to Auru, there was originally a path to the desert, but it was closed off. As a result, this is one of the areas where Link cannot summon Epona. This may make crossing the vast desert rather difficult, but there are some Bullbos in a nearby Bulblin camp Link can ride, or he can travel in his wolf form, which is faster than his Hylian form.
Interestingly, the map of Hyrule has the words Great Desert, rather than Gerudo Desert, spelled in Hylian.
The Gerudo Desert is a region located in the Gerudo province of Hyrule in Breath of the Wild. Gerudo Town and the Kara Kara Bazaar are located in this region, as well as the Great Fairy Fountain where Tera found under the Gerudo Great Skeleton. The Gerudo Desert is also the endemic location of the four Molduga and a rarer subspecies called Molduking which are among the desert's top predators as they eat anything they can catch including Treasure Chests. The Divine Beast Vah Naboris is encountered in this region. The East Gerudo Ruins is dedicated to the Seven Heroines the divine protectors of the Gerudo people though a rumored Eighth Heroine is worshipped in the Gerudo Highlands by a certain sect of the Gerudo population. The sand covered ruins of the Arbiter's Grounds can be found in the southern part southwest of the Southern Oasis and east of the Gerudo Great Skeleton. The Gerudo once again inhabit Gerudo Desert ruled by a line of female chieftains, currently Riju. Due to its remoteness it weathered the Great Calamity with the Gerudo remaining loyal to the fallen Kingdom of Hyrule engaging in free trade with Hylians and other races.
Sand Seals are native to the region and have even been domesticated by the Gerudo for Sand-Seal Surfing the main form of transportation besides travelling on foot. Like the Haunted Wasteland in Ocarina of Time, Horses refuse to enter Gerudo Desert via the Gerudo Desert Gateway from Gerudo Canyon. The desert itself is surrounded by the cold and often snowy Gerudo Highlands with Gerudo Canyon being the main route into the desert. Unlike Gerudo Desert, the Gerudo Canyon Pass receives more rainfall and is connected to Hyrule Field by the Digdogg Suspension Bridge, housing the Gerudo Canyon Stable
Gerudo Desert is a dry sandy desert where rainfall is practically non-existent and sandstorms are common especially as one travels further into the desert. It is trecherously hot in the day and dangerously cold at night. Hydromelons, Voltfruits, Spicy Peppers, and Palm Fruits are native to the region along with all three species of Safflina. Herons, Sand Sparrow, and Wasteland Coyote are the local fauna. The desert sandstorms prevent Link from travelling outside the map by walking too far west, south, or southwest.
Gerudo Desert is a location that appears in Hyrule Warriors and Hyrule Warriors Legends. In the story, after the seal on all four of Ganondorf's Spirit Fragments have been removed and Ganondorf is fully revived, he returns to the desert of his birth raise an army to take back his Triforce of Power and acquire the other two pieces held by Link and Zelda. Reviving Ghirahim and Zant to serve as his generals, he begins his quest by defeating a group of monsters based in the desert and force the rest into submission. After raising his army, Ganondorf leaves the desert and reclaims the Triforce of Power from Lana (which she had claimed after Cia's death) in the Valley of Seers. He then invades Hyrule Field and after defeating both Link and Zelda, obtains the complete Triforce. Confident in his victory, Ganondorf disappears, while his Generals and army return to the desert. Undeterred Zelda, Link, and Lana lead the Hyrulean Forces into the desert to defeat Ganondorf's generals. They manage to secure two oasis found in the desert and confront both Zant and Ghirahim, who are defeated. However despite this, Ganondorf's Forces continue to fight and eventually manage to surround Lana, who uses her magic to summon their allies from across time (Darunia, Ruto, Agitha, Midna, and Fi) which turns the battle in the Hyrulean Forces favor. It is eventually revealed the Ghirahim and Zant they had defeated earlier where fakes and that the real ones had been leading Ganondorf's Forces from their hiding spot inside the Arbiter's Grounds. Ghirahim and Zant are eventually defeated restoring hope and boosting moral of the Hyrulean Forces, leading to the final showdown with Ganondorf at Ganon's Tower.
Given its location and name, it is likely that Gerudo Desert was originally the Haunted Wasteland from Ocarina of Time. Apparently some point after the events of Ocarina of Time, the desert region became cut off from the rest of Hyrule (either by geologically activity, by Ganondorf and/or the Gerudo during the King of Thieves rampage across Hyrule, or by the Kingdom of Hyrule and/or its allies). Following Ganondorf's capture, the Gerudo where either expelled/banished from the desert and/or condemned to imprisonment within the Arbiter's Grounds or lived in an area of the desert isolated from portion the Hero of Twilight explores. Alternatively the Gerudo became intergrated in Hyrulean society through reproducing with the Hylian and Human population as Breath of the Wild confirms Gerudo primarily reproduce with Hylian men due to Gerudo men being an extremely rare occurrence and Ganondorf's capture and imprisonment effectively robbed the Gerudo of their race's only living male.
In Breath of the Wild, there are several features in common with the Haunted Wasteland. Gerudo Desert has sudden Sandstorm that make navigating the desert difficult and/or certain areas inaccessible. Layout of the southern desert's Great Fairy Fountain and Southern Oasis resemble the Desert Colossus area with the Arbiter's Grounds in the same general location as the Spirit Temple supporting the theory that the Spirit Temple was converted into the prison. However the Arbiter's Grounds has apparently been long abandoned with its ruins being left to be consumed by the desert sands. Additionally all horses including Epona refuse to enter the desert even by using horse steps, much like how Epona refuses to enter the Haunted Wasteland in Ocarina of Time. However it is unclear if these are simply references or evidence that Gerudo Desert was once the Haunted Wasteland which may be true as Breath of the Wild is officially confirmed to take place some time after Ocarina of Time in an indeterminate timeline.
It is possible that Gerudo Desert was originally Lanayru Desert from Skyward Sword. The Lanayru Desert region, could have eventually become the desert region in Ocarina of Time and then Gerudo Desert in Twilight Princess and Breath of the Wild. However as Lanayru Desert was once a fertile land and sea area before the modern era of Skyward Sword its possible the two deserts are unrelated and separate deserts created by Hyrule's ever changing geology and geography.