Normally miniature copies of the magus that he uses to perform tasks (flexible in accordance with the thought patterns of the magus) while busy working on his research. Acts as the magus would as if it were a part of him, although it is an independent entity (which is generally the best type of familiar). The symbol of the magus itself and fundamentally different from creatures binded by summoning and contracts. Physical and mental connections exist between the magus and the familiar.

Takes too much work to make a human being familiar from scratch, as well as to maintain it, which is why small animals are preferred, like dogs, bats, or cats.

Basically an aspect of the magus with the same knowledge but different personality and form of reasoning to serve as another way of gaining a different perspective on things.

Can be prepared by placing the lingering remains of a person's soul into the body of a dead animal. The soul is used to allow the smooth formation of a personality. This isn't resurrection, though. The resulting creature is something totally different. Following that, the corpse is repaired and a connection is added to the corpse to make it an extension of oneself, which is accomplished by moving parts of the practitioner's flesh (the parts where circuits are particularly strong in the caster; eyes, hair, blood, etc) onto the animal.

The resulting familiar will gain circuits that the original animal had never had before and can use spells just like the magus who created it. However, Prana cannot be created independently. This is supplied by its creator through their spiritual line. Hence, the magus is needed for the familiar to cast spells as well as survive. Some of the abnormally powerful familiars (those like Len who have a demonic aspect) can overcome this and form contracts with others to survive if their creator dies. These can also take Prana through other methods if they have no master.

That of course is only one type of familiar and many magi really don't like that method. Actual living animals can be binded to be made into familiars instead as well. There are also those that would make a familiar out of another living human being, but that's seen as monstrous. Also, familiars without souls can be used; however, the modern versions of these are weak.

In terms of relationship, the ideal familiar is not supposed to act without the orders of the magus.

Transference of consciousness into familiars is possible. Hence, the magus can use them like remote control units for recon or exploring. However, this isn't possible with familiars that have souls as they are the ones that are controlling the body. Just obtaining a video-feed from the familiar is also possible (like Kotomine did with Lancer in HF).

While it is possible to transfer one's consciousness/soul into a creature with an existing soul, this is nearly impossible. Even transference into a familiar without a soul doesn't mean that the magus has completely transferred himself. Destruction of the body (this also includes through natural means like aging) of the magus will mean the destruction of the soul of the magus. There are ways to get around this, for instance, complete transference using the Dress of Heaven, resurrection (Roa), or vampiric methods that Zouken had resorted to (and even then, it's not clear whether Zouken transformed or transferred his main body into a collection of worms).

Nrvnqsr's 666 beasts (or rather body itself) are also familiars. What makes these particularly different from other familiars are that they all are generally equal in power (each is Nrvnqsr himself would be one reading of it in relation to the above).

Slime
スライム
Used by Alba. He really should have joined one of those special effect crews that work on horror movies.... Made of Ether.

Inchuu
淫虫 - Inchuu
The lowest of familiars. Used by Zouken. Worms that love feasting on the blood, marrow, and energy of humans. Will shatter the spine of males and suck on the brain, turning them into cripples. Will feast on the mental energies of the women instead by sexual stimulation through the nervous system. Will not normally eat the flesh of women, but the uterus is one of their favorite meals. Will consume the placenta once sexual pleasures, enough to fry the nerves in the brain, are given to the victim.

Dragon Tooth Warrior
竜牙兵 - Ryuugahei

A familiar made from the fangs of dragons. Scatter the fangs on the grounds and out'll come disposable footsoldiers that'll gain the Prana of dragons and knowledge from the earth. Will be familiar to those pen and paper rpg oldtimers. Really strong actually. A level 5 adventurer trying to take one out will probably be killed instead. From the legend of Cadmus.

Vampire familiars
死者 - Shisha
The deceased. Corpse. A dead person. Or, "Those who are not alive anymore Lololol". Basic point. Soulless puppets that won't move or act without a head honcho behind them. It really is just a dead person that's being used as a familiar.

The familiars vampires use. A person that gets their blood sucked out by a vampire is going to die from that. But. Send your own blood into the person you're sucking blood out from, and the dead person can be used as a puppet.

Pretty much those who are being controlled completely as extensions of the vampires when the whole process of revival into a bloodsucker (ghoul to vampire) that a human would undergo is ignored.

Not so much as the soldiers of the vampire, but 100% puppets/ants that are connected to their creator, unlike ghouls and such. Meat is consumed in order to maintain their bodies, but more than half of that energy is transmitted over to the vampire.

Several ranks stronger than the living dead, but still mindless and soulless.

Len
レン - Ren
An unusually powerful familiar formed from the remains of a human soul and the corpse of a cat.

Projection machine
幻燈機械 - Gentou kikai

One of the familiars Touko made to replace the familiar that her sister destroyed. An orange suitcase that operates like a projector, shaping an ether clump into a monstrous shadow cat. The cat itself will not be destroyed unless the suitcase is destroyed. Has the ability to heal Touko if it overlaps on her. Seriously. A ghost liner type?

The Sealed Box
封印の匣 - Fuuin no hako

The second of Touko's current familiars. A black monster in a box with thousands of mouths and thorn like tentacles. Drags the poor sucker inside and eats it. A Ghost Liner possibly?

Shadow Giants
影の巨人 - Kage no kyojin

Sakura's familiars. Normally they would be extremely small, but when she is functioning as a grail, they become humongous. The Prana composing their bodies is around some 1000 each. Plus, they're really just a big materialized curse due to Angra Mainyu corruption. You wouldn't want to get in contact with one of these. A Ghost Liner possibly?

Black hound
黒い猟犬 - Kuroi ryouken
A black Doberman. Alba's familiar. Which didn't show up in Rakkyo, but he or she was around. Alba, who can't love other people, was really fond of animals that could love others easily. Alba looks quite like the main character (instead of the throw-away character) when he struts around in town wearing a red long coat and a silver hat, with his black Doberman at his side.

Owls
梟 - Fukurou

Used by Rin for recon. Made of amethyst.

Ghost Liner
ゴーストライナー -

The greatest of familiars. Servants are pretty close to this type.