The Chandrian are a group of seven beings, possibly Ruach, known in myth, folklore, and children's stories throughout Temerant. They are also known as the Nameless, Rhinta, and the Seven. They are led by one known as Haliax, who is known to be formerly called Lanre and is known to the Adem as Alaxel. The others serve Haliax in part through fear, as Haliax protects them and also holds power over them, using them "as tools." They do not always travel together, and Haliax seems to do so in order to maintain order within the group.
While they have a purpose, it is unknown, adding to their air of mystery and making them more terrifying, for none know why they do what they do. 
Little is known about the Chandrian, other than that they are universally seen as evil and have signs associated with them. They go by many names, though "Chandrian" is one of the most common. What these signs are is subject to great debate. In most cultures, they are seen as mythological beings, and it is often accepted that seven people or beings make up this group, though some sources claim there to be ten. It is believed they root out and destroy all mentions of themselves, possibly because they are on the run from the Amyr, who may know their weakness.
Who keeps you safe from the Amyr? The singers? The Sithe? From all that would harm you in the world?
They are widely feared as cruel creatures with an unknown purpose behind their evil actions, though Haliax appears to hold disdain for cruelty. In an Adem poem, he is referred to as "sane," which may suggest that the others have succumbed to madness, possibly the cause of their cruelty.
You are too fond of your little cruelties. All of you.
– Haliax to Cinder & the Chandrian
Their name comes from the Temic word "Chaen-dien" meaning "seven of them," which is one of the strongest arguments for there to be seven beings in the group.
Kvothe's father, Arliden, and later Kvothe uncover several signs that are to signal the presence of the Chandrian. It is wildly suggested that blue-flame indicate their presence, but others are more circumspect, and blue-flame can be recreated chemically, as Arliden and Laurian have Abenthy do to use in plays. Arliden and Laurian disagree on several accounts of the signs; Laurian suggests that each Chandrian has their own sign, explaining why there are disagreements in what the signs are; if different Chandrian are present, different signs will be seen. Many of these are considered to be "accelerated entropy." Kvothe personally experiences these in his early life, to include blue flame, rusted metal, blight, and darkness. He may have experienced others but not attributed them to the Chandrian. These others include madness and silence, though these may be circumstantial rather than actual signs. Decay of various sorts (rust, wood rot, crop withering) and like negative effects appear to be a common theme.
Signs may or may not be external effects with a purpose; darkness around Haliax appears as an intense shadow that can even keep sunlight or firelight from reaching him; his cowl is visible, but his face s totally obscured. 
Confirmed Signs: 
- Blue flame (Sign of Cyphus)
- Decay and rot (of wood) (Sign of Usnea)
- Complete rusting of iron and steel (Sign of Stercus)
- Cold (Sign of Ferule)
- Dark Eyes (Sign of Cinder, aka Ferule)
- Shadow like a dark fog (Sign of Haliax, aka Alaxel), appears to be capable of teleporting those who enter it.
- Blight (Sign of Alenta)
- Madness / Shock
- Darkness / Moonless Night
- Silence (Sign of Dalcenti)
The Adem have a poem assigning each of the Chandrian to their sign:
Cyphus bears the blue flame. Stercus is in thrall of iron. Ferule chill and dark of eye. Usnea lives in nothing but decay. Grey Dalcenti never speaks. Pale Alenta brings the blight. Last there is the lord of the seven: Hated. Hopeless. Sleepless. Sane. Alaxel bears the shadow's hame. 
Of these, based off of Kvothe's experience , it is strongly believed that one referred to as "Cinder" is the poem's "Ferule" and Alaxel refers to Haliax; Haliax exercises his power over Cinder by speaking his name, "Ferula."
These signs are also described in children's songs. The only other descriptions Kvothe has uncovered were from Nina, a girl from Trebon, who described and later drew a relic. However, she only saw one side of the vase, and so was only able to describe three of the eight figures; the seven Chandrian and a member of the Ciridae. Kvothe believes these three to be Cinder, Halifax, and an Amyr. In the drawings Cinder is depicted with black eyes, standing in water and surrounded by snow. Haliax is shown with a waxing moon and two candles, one bright and the other shrouded in shadow. She also remembers additional figures in less detail, a nude woman, a broken sword, and a fire.
It has been suggested that the Chandrian may be able to at least partly mask the signs that reveal their true nature using the fae magic known as glamourie.
These attributes are confirmed further through a series of stories: We are introduced to the frame-story's patrons of the Waystone Inn with Old Cob's telling of Taborlin the Great, trapped in a stone room with no way out - he places special emphasis to note that the lamps were burning blue to strike fear into his listeners, indicating the well-known Chandrian early on in the Frame Story; the sign of Cyphus. 
This Cyphus is likely the same Scyphus found in Marten's story of Taborlin, where he tells of Sorcerer-King Scyphus, who had trapped Taborlin in a room of stone whereupon he escapes by the power of naming and in both stories he is initially deprived of his tools. While Marten's story does not mention blue-flame, likely lost due to the "childish" relation to the Chandrian, and Old Cob's story does not mention Sorcerer-King Scyphus, likely due to Newarre's general lack of knowledge of outside locations, nobility, and history, they are most likely the same. These stories, coupled with the above Adem poem, gives credit to the tales of the Chandrian and their signs, also suggests that Taborlin was one of their great enemies. This is further propagated by Taborlin's use of a copper-sword; copper may be nameless, but it would also withstand the sign of Stercus, who rusts iron.
In addition to their signs, the Chandrian are known to be able to use glamourie, a Faen magic. Kvothe encounters Cinder when assaulting a bandit-camp, but does not recognize him as he is hidden under a glamourie.
In this instance, Cinder shows himself to be capable of shrugging off injuries that would greatly wound a human when Marten shoots an arrow with such force that it pierces his armor, entire leg, and armor on the opposite side of the leg. Cinder merely breaks the arrow in half and pulls it out and thereafter appears entirely uninjured. While this resilience may be relegated only to Cinder, it is likely an attribute of all Chandrian.
Yet again in this encounter, Cinder shows the ability to hear things humans cannot; Kvothe believes he is hearing the prayers of Marten, but it is likely that he is hearing or otherwise sensing the approach of a foe he does not wish to fight, looking skyward. Kvothe remarks that the tilting of his head backward, as if listening, is familiar, referring back to his first encounter as a young boy, when the Chandrian note the approach of another group and immediately flee via the shadows of Haliax, which cause them to disappear, either teleporting them away or moving into the Faen realm.
The Chandrian can hear when their names are spoken, which is how they were able to track down Kvothe's troupe. Bast confirms that this is an ability that "some things" have, suggesting that this is not exclusive to the Chandrian. This may be why Cinder was forced to flee the bandit-camp in the Eld; Marten's prayers to Tehlu may have called Tehlu and his angels, the suggested opposition to the Chandrian.
Most references to the Chandrian do not come from credible sources, but even in these there may be valuable information. Of these lesser credible sources, we see additional signs than those shown above, such as thunder, rainbows, and darkening of the moon. Of these, only the last maintains any credibility or cross-referencing. Several of these go on to make fanciful claims, such as their living in the clouds, dreams, or a castle made of candy. It may be valuable to keep in mind that while these may not be literally true, they may allude to truths, as many stories are based in fact.
In The Book of Secrets which Kvothe finds in the Dead Ledgers of the archives, the author writes this about the Chandrian:
The Chandrian move from place to place, But they never leave a trace. They hold their secrets very tight, But they never scratch and they never bite. They never fight and they never fuss. In fact they are quite nice to us., They come and they go in the blink of an eye, Like a bright bolt of lightning out of the sky.
The first half and last two lines of this passage reinforce familiar notions of the Chandrian; that they move around quickly, likely with the aid of Haliax's mastery of shadow, and are adamant about their secrets. The second half goes against other information laid out about them, as they appear to do great violence for little reason or no reason at all. If the The Book of Secrets is to be believed, the Chandrian may have changed personality, membership, or tactics for any number of reasons. It is also possible that the book was poorly translated or intentionally altered.
A Quainte Compendium of Folke Belief is made to sound a little more credible. It notes that the Chandrian are universally feared by all as no other presumably mythical creature is. The book also confirms their number (seven) and their apparent lack of motive. It similarly mentions their signs; darkness of the sun (to mirror the darkness of the moon - or likely, darkness of any sort), wine going sour, blindness, crops withering, unseasonable storms, and miscarriage. 
There is also a common children's song which appears to confirm the nature of blue fire, darkness [of the face of Haliax], and ability to apparently teleport via shadow, which are a few of the signs confirmed by Kvothe.
When the hearthfire turns to blue, What to do? What to do? Run outside. Run and hide. When his eyes are black as crow? Where to go? Where to go? Near and far. Here they are. See a man without a face? Move like ghosts from place to place. What's their plan? What's their plan? Chandrian. Chandrian.
Of all the seemingly nonsensical folktales and songs, this may be the most truthful. Blue fire, blackness, black-of-eye, mysterious travel and equally mysterious plan are all confirmed by other sources. It also does not name any Chandrian by name, thereby preventing calling them, and the instructional bears the likeness of what may be told to children in an easy-to-remember song in an era where the Chandrian were more of a threat. As it contains rhymes that would be broken with any inaccurate repetition, it is more likely than other tales to have survived the ages.
- The Name of the Wind, Chapter 16, "Hope"
- The Wise Man's Fear, Chapter 128, "Names"
- The Name of the Wind, Chapter 1, "A Place for Demons"
- The Wise Man's Fear, Chapter 83, "Lack of Sight"
- The Wise Man's Fear, Chapter 91, "Flame, Thunder, Broken Tree"
- The Wise Man's Fear, Chapter 129, "Interlude — Din of Whispering"
- The Wise Man's Fear, Chapter 14, "The Hidden City"
- The Wise Man's Fear, Chapter 16, "Unspoken Fear"