Twili

The Twili are a race of beings who inhabit the Twilight Realm. Most of the inhabitants are turned into "monsters" due to Zant's evil rule. While Midna and Zant are the only Twili that appear of whom with 100% certainty can be said that they appear as they should be. All other Twili that are briefly seen in  Twilight Princess were quite different in appearance, resembling Midna in her cursed form more than Zant and Midna in her true form. As such, some assume that the curse on the Twili had not been completely lifted at the time Link met them.

Background
Eons ago, the Twili were a group of dark sorcerers, ethnicities unknown, that were sent to the Twilight Realm by the Sages of Hyrule as punishment for their misgoverned attempt to use old magic to claim the Triforce. Their "old magic" became known as the Fused Shadows, a powerful instrument, however, their powers proved too weak for the power of the gods. They were banished and their Fused Shadow was split into four pieces and scattered throughout the two realms, The Twilight realm and Hyrule. This tribe lived in the Twilight Realm for centuries until evolving, mere shadows of what they once were, the Twili tribe became used to their surroundings and came to accept their fate. While some came to love the beautiful peace that can be found only in Twilight, it drove some of it's inhabitants mad. After centuries of rule, Princess Midna became just one of many rulers in a long line of royalty, the Twilight Princess. It was around this time that a rebel force grew from within the Twilight, spearheaded by Zant. It is revealed that Zant was next to become Twilight Ruler, but was passed over. In a terrible rage, he used the power of his false-god, Ganondorf, to transform most of the inhabitants of Twilight into monsters. Zant also transformed Midna into an imp creature as a form of humiliation. Midna's only hope was to find the magic of her ancestors, the Fused Shadows, and use it against Zant to save the realm.

The Twili in  Twilight Princess are usually seen as enemies, however when Link goes to the Palace of Twilight, he reverts several of the Twili back to their true forms. The Twili have strange glowing markings on their skins, which are a blue/grey tinge mixed with black, this complexion may be due to lack of full light as the Twili have changed from what they were when they were ejected from the "World of Light". They also have oval, yellow eyes and are (usually) quite thin and lanky.

Midna's true form seems to be quite a lot more human-like than this as she has distinct eyes and has many other different characteristics that differ from the Twili. This could be due to her lineage as their may be a separate sub-species of Twili in the Royal Family that have more human qualities in them. It is quite possible that once Ganondorf is killed, and Zant's spirit dies, that the Twili race as a whole are turned back into beings more resembling Midna and Zant.

Timeline, Ocarina and Majora's Mask
The events described in Twilight Princess are likely to have occurred before the events of Ocarina of Time, which is generally believed to be near the beginning of the timeline in Zelda game. This is because the Twili's ancestors' are described as trying to assert dominion over the Sacred Realm before the Triforce had ever been successfully found, and as the Triforce has been split by the time of Twilight Princess, claimed as being several decades after Ocarina of Time, it is likely that it was found during Ocarina of Time. Furthermore, the Twili's ancestors are described as having been imprisoned long ago, long enough for their race to lose all passion and ambition.

Though it has been theorized, Twilight Princess makes no mention of Majora's Mask. Debates arose when similarity between the eye-design of Midna and Majora's Mask were alleged by a number of fans, and now some players choose to speculate that the Twili are in fact responsible for creating Majora in a separate attempt to obtain the Triforce. However, this is contradictory, as the Twili were imprisoned by the Light Spirits for abusing their magic, while the ancient tribe that used Majora's Mask chose to seal it themselves.

Others still believe that the Twili are ancestors or descendants of the Zuna Tribe see in Four Swords Adventures.