Wraiths (魔獣,Majū, lit. magical beasts) are manifestations of grief in the new world recreated by Madoka Kaname. They replace the witches that magical girls must fight. They resemble tall, statue-like humanoids wearing robes with no visible limbs (though concept art shows them as having hands that shoot thin lasers to attack). Their faces are partially covered by digital polygon-like shapes that appear to glitch out randomly on or around their being.
Wraith Creatures that emerged in a world without Witches to steal human emotions. They lack any will of their own and move only as a swarm. Much about them remains shrouded in mystery, but one thing is for certain — they exist to maintain the balance of the universe.
Acolyte Wraith Slightly stronger than normal Wraiths. They're burning hot ones. They generate swords that they throw from their palms or attack with flaming spears.
Enlightenment Wraith Stronger than Acolyte Wraiths. Uses block-shaped organs to crush things. When one appears, it changes the terrain — metal erodes, machines become useless, and it really dries your skin out.
Deliverance Wraith Stronger than normal, Acolyte, and Enlightenment Wraiths. The most powerful Wraith. They're really, really cold and apread rigid air. Nagisa has never encountered one, but is pretty sure she really hates them.
Wraith—Sayaka & Kyoko They are Wraiths that used Homura's memory manipulation magic to mimic humans from a Magical Girl's memory. It seems they can use time manipulation as well. However, to deceive and entrap people... isn't that what a Witch would do rather than a Wraith?
Mutant Wraiths: These wraiths are created when they absorbed part of Homura's memory and time manipulation powers, without being able to convert them into grief cubes. They can take on the form of people close to their targets which are based on their memories to trick their victims. When attacking, they revert to a more wraith-like appearance. Examples include Wraith forms of Mami's parents, Sayaka, Kyoko, Mami herself and Wraith Madoka, who have all appeared to different characters in the series. Due to this disguising ability originating from Homura's memory manipulation magic, only the people who knew those impersonated could be fooled by their disguises, as others see them as wraiths. They also had the power to momentarily stop time to attack, which initially appears as super-speed to others.
Wraith—Madoka It's a Wraith that appeared in front of Homura and calls herself "an ally of Homura-chan". It gives a feeling that it has sort at of ego, unlike other Mutant Wraiths. I get the impression that this Wraith lacks of words compared to the Madoka I know. Perhaps it doesn't have any communication skills.
Wraith Madoka: A special mutant wraith that took the form of Madoka and claimed to be an ally of Homura. This wraith was more sentient than others and could communicate telepathically. As it spent more time with Homura, it absorbed more and more of her emotions, even gaining the power of momentarily stopping time herself.
A giant wraith mutated by the curse inside Homura's shield. The Spindle Witch is both a wraith and not, being an incomplete witch and serving as a manifestation of calamity. It can instantly kill anything it touches and exerts an immense cold that balances the heat stolen from other beings.
The Spindle Witch's minions which resemble both Homura and Deliverance Wraiths. They are mass-produced and attack with energy beams.
History
Anime
Original Anime
Wraiths first appear at the post-credits scene of episode 12 of the original anime after Madoka's wish erases all the witches and Homura Akemi is seen fighting several of them afterwards. It is shown that in the new world, magical girls now fight wraiths instead, which are merely a different form of curses born from humanity.
They appear to travel in large groups and do not reside in barriers, mostly appearing at night, unable to be seen by normal people. It is implied by Kyubey that they give off miasma in the air, which supposedly points to how many are in a single area. When defeated, wraiths drop (possibly several) small, cubic fragments of their grief similar to witches' grief seeds that can be harvested by magical girls to clean their soul gems and combat entropy (though Kyubey points out that this comes at the expense of energy efficiency).
Wraiths feature prominently in the manga spin-off Puella Magi Madoka Magica: Wraith Arc, where they serve as the main antagonistic forces and sources of conflict in the plot, outside of the characters' interactions with one another. Wraith Arc also gives more information on the nature, behavior, and types of wraiths. Wraiths are shown to be able to affect soul gems (as performed on Sayaka Miki), steal away magic powers (as performed on Homura Akemi), take objects (stealing Homura's ribbons from Madoka), and even take on the forms (including memories and intelligence) of magical girls and possibly other human beings.
Abilities
Wraiths possess various powers and abilities, making them formidable enemies for magical girls:
Teleportation: Wraiths can teleport from one place to another, allowing them to ambush opponents or escape when threatened.
Invisibility: Much like Kyubey and witches, wraiths are invisible to regular humans, only magical girls can see them. Their ability also masks the presence of magical girls while fighting, which helps keep the existence of magical girls a secret.
Emotion Siphonage: Wraiths are attracted to unstable emotions and feed on the emotional energy of humans and magical girls. If they consume someone’s heart, that person becomes an emotional shell of themselves. The emotional energy is then converted into a "safe form" as grief cubes and when the wraith carrying them is defeated, they're left behind. However, the cubes are less effective than grief seeds in purifying soul gems and contain the emotional energy collected from people in a purified form.
Emotion Detection: Wraiths are particularly drawn to the strong emotions of magical girls, especially those with unstable emotions. If a magical girl’s emotions are highly unstable, the wraiths can encase her in a cube while taking a praying position, draining her emotions and making it difficult to escape.
Aura of Cold: Some wraiths, particularly the stronger types, exude a cold aura that can freeze objects in their surroundings.
Beams and Projectiles: Wraiths primarily attack magical girls either by shooting energy beams from the glitching around them, or through shooting swords from their palms.
Grief Cubes
Homura cleaning her Soul Gem with Grief Cubes
Grief Cubes are the equivalent of Grief Seeds in the Wraith Arc universe. Just like Grief Seeds, they drop when Wraiths are defeated and can be used to purify the Soul Gems of Magical Girls.
Grief Cubes are made out of human emotional energy, consumed by the Wraiths, and later purified, giving form to Grief Cubes. The Cubes are less effective than Grief Seeds, but drop in greater quantities.
Observations
Because Madoka's wish only erased witches, grief was not removed from the new world as Madoka didn't change human nature. As a result, the wraiths are distortions of Madoka's cause and effect of her wish, and give magical girls other means of obtaining grief seeds to clean their soul gems and combat entropy.
Wraith types are named after Buddhist levels of enlightenment.
Shugen is a Buddhist-adjacent term referring to a form of asceticism that involves becoming one with nature/kami/the Tao (the practice tends to be syncretic). A Shugenja (practitioner) is an ascetic mountain mystic, one who undergoes severe physical and spiritual training in the wilderness to acquire supernatural powers. They are often seen as itinerant monks or yogis.
Satori is the Japanese Zen Buddhist term for spiritual awakening and is often translated as "enlightenment." It is different from Buddhahood, as it's more about understanding one's own nature, which in itself is just a step towards complete Buddhahood.
Moksha is a central concept in Hinduism, Buddhism, and Jainism. It means emancipation from earthly desires and the ultimate spiritual goal in these traditions. It is freedom from the cycle of reincarnation (Samsara), and thus freedom from all worldly suffering, desires, and the illusion of the self. Unlike Nirvana, a person undergoing Moksha hasn't died yet.
Normal Wraiths also themselves resemble novice monks or Postulants (Śrāmaṇera), who wear identical robes, shave their heads and let go of their personal identities.
The Wraiths seem to resemble "moirae" from Greek mythology, beings that personified the inescapable destiny of humanity.
The Wraiths battled in Magia Exedra resembles to the skeletal ones seen in the manga concept art.
Trivia
Early fansubs of the anime called wraiths "demons". The name of "wraith" comes from the official translation of the anime.
The official translations of the original series' first manga versions refer to them as "magical beasts". It should be noted, however, that the official manga translations are already inconsistent with the official anime translations.
While defeating a wraith that has stolen someone's emotions won't instantly return them, victims may gradually regain their emotions over time regardless. At least, this was implied by Mami to be the case with magical girls, telling Homura to grow stronger to compensate for her lost magic.