The Cephalopods are one of the three known biological sentient beings, the other two being the Humans and the Incubators. Little was known about them from Volumes 1 through 3, but from Volume 4 onwards a much larger amount of knowledge became available.
Volumes 1 to 3
Their existence was unknown to mankind up until the invasion of the Aurora Colony, in which they arrived unexpectedly and killed every human in sight. Shortly later, Governance redistributed a considerable amount of Allocs and representation to the war effort, but it was of little help, as the Cephalopods destroyed the Atlas Colony with the same ease. The tide of the war was only reversed with the involvement of Magical Girls, who realized that humanity had little hope of defending itself and decided, through the MSY, to stop hiding and fight themselves the invaders. In the Battle for the Colony World of New Athens, in the Epsilon Eridani Sector, humanity had its first victory, as the humans, led by Akemi Homura, successfully held off the invading force.
Nothing was found out about their motives for attacking, but a considerable amount of empirical knowledge was gained through the Contact War. Biologically, they resemble both humans– with bipedal locomotion, rudimentary skeletons, water-retaining skin, forelimbs that spread into multiple grasping appendages, and eyes that have noticeable sclerae– and octopi– with a decentralised nervous system, multiple limbs, rubbery skin and a ring of tentacles around the mouth. Scientifically, they're much more advanced than humanity, having better technologies for FTL engines, stealth, forcefields and dominating the use of wormholes for instantaneous travel. As to their war strategies, they range from the shockingly practical, e.g. implanting self-destruct modules on their soldiers to avoid the theft of technology and showing little hesitation in sacrificing their own units for tactical advantages, to the seemingly nonsensical, such as attacking the less valuable target when there's more than one available and other tactics that make little sense to human strategists.
It was found out at the very end of Volume 3 that there was an attempt at diplomacy before the deflagration of the war, with representatives from the Cephalopods meeting with members of the Directorate, but those memories were erased, either willingly or through a breach in the TCF.
Their home planet is called Great Sea, a planet in the Triangulum Galaxy with temperature and relative air humidity nearing the 40°C and 100% marks. They have a symbiotic relationship with a species similar to terrestrial penguins, that was maintained even as they began their exploration of space.
The history of their languages has five main phases, respectively: Pre-Linguistics, Touch-and-Display Languages, which used both the chromatophores in their skin and limb movements, Written Scripts, Electronic Transmissions and Telepathic Channels, the phase in which they're currently at. Their official language is multi-channeled and concurrent, as opposed to the single-threaded and back-and-forth aspects of usual human languages, and they call themselves the Thinkers.
Another unique aspect of their communication is empathize-open, the request that an interlocutor share their preference-specification, or pref-spec for short. A pref-spec is comprised of the moral values, or preferences, that a individual has. Its introduction into Thinker society brought on a full-species war between those who defended that empathize-open should always be allowed upon request and those who considered making it mandatory an unacceptable violation of privacy.
The faction in favor of making empathize-open universally obligatory won, and, in another parallel to the human Unification Wars, a pan-species government called Consensus was then installed. The Consensus is divided in functional units called Tentacles, but, unlike the human Directorates, the scope of a Tentacle isn't an abstract aspect of society (such as "Science and Technology" and "Military Affairs"), rather it is a group of individuals with similar pref-specs (e.g. "Ahimsa-extending" or "Thinker-preserving"). Much like human Governance, the Consensus arbitrates disputes between Tentacles with opposing interests and makes species-wide decisions.
Their moral views on technology use are markedly different from those of Governance. They oppose neither the backup of organic consciences into electronic devices nor the use of organic bodies controlled from afar as soldiers. But they're markedly against the creation of single-purpose AIs, preferring to appoint those already better-suited for the task at hand.
Blood and Ichor, for their biology
The Dying Light, Part Two, for their technology
Aftershocks, for their society